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208 volts
208 volt is usually derived from commercial 3-phase transformer configurations.
There are a wide variety of voltages across the world.
Voltages are a function of power generation, mathematics of electricity, availability of conductive materials, cost, safety, and need for standardization.
Standardized voltage means mass production of electric wire, switches, and appliances is possible.
Voltages vary across the globe, and as a result appliances that work in Australia might not function in Americas etc.
208 volts is a standard voltage available in the Americas, usually found in commercial applications such as business or apartment building.
End-user voltage is specified by the builder or designer according to normal practices, and then the power company installs the correct transformer.
Power company transformers come in a wide variety, and are manufactured to standard specification. Transformers are basically 2 coils of wire, each coil having a different number of winds around a steel core. Fewer winds on one coil and more winds on the other cause voltage to change. The transformer determines the final voltage that is available at the end user location.
For example a typical house has 1 transformer that converts single-phase 7200 volt distribution line into in 120-240 volt for household. The power company connects 7200 volt to the primary coil, and that produces 120-240 volt on the secondary coil. This is how specific voltages are achieved.
Likewise, each business has transformers, except they have 3 transformers instead of 1. This is a three-phase service, and is generally the source of 208 volt. The power company installs specific transformers, then connects three-phase 7200 volt distribution line onto the three transformers on the primary side. The resulting voltage on the secondary side is also three-phase. Depending on which transformers are used, and how they are wired, the secondary voltage can include 208 volt. This is where 208 volts is typically found; in commercial 3-phase and not residential single-phase. However, single phase 208 volt can be wired from 3-phase installation. So 208 volt is available in 3-phase or single-phase depending on the specific installation. It sounds complicated, but in practice, the methods for specifying voltages and achieving the wiring needed are standardized and well known among electricians etc.
Different transformers and different wiring configurations allow a selection of voltage choices for business and industry. Usually, there are no choices for homes, and 120-240 is standard. This means you would more likely encounter 208 volts in a building or apartment complex, but not at a residential house.
It all starts with standardization, and is determined by the transformer(s) at each location.
water heater label
Single-phase 240-208 water heater 
208 volt as it applies to water heater
All appliances have a label.
The purpose of a label is to specify what voltages can be used with the appliance.
Typical residential water heater label shows 240-208 rating. This means the water heater will work with 240 volt or 208 volt.
Note if the water heater is connected to 208 volt, the wattage of element drops to 4125 watts. This is because the water heater comes with elements rated for 240 volt, and because elements are like light bubs. When household voltage drops, the light bulb becomes dim. Same with water heater element: when 208 volt is applied to 240 volt element, the element burns a bit cooler and heats slower. Each element has a rating that appears on the end.
In the very unique case of water heaters, you can connect 120 volts to the 208-240V heater. So voltages lower than the highest rating are ok, but this applies to water heaters and not other household appliances.
The reason residential water heater will work with 120-208-240 volt is the elements are resistive (like a light bulb) and the thermostats are mechanical. 
If the water heater is connected to higher voltages, such as 480 volts instead of 208-240, the elements will burn out because the elements are rated for 240 volt maximum. If the elements are changed to 480Volt rating, the water heater will function correctly using same thermostats etc, but the label must be changed on water heater to meet code.

Electrical equipment and timers that are rated for 240 volt are often rated for 208 volt. But do not assume. Always check the label. Connecting to wrong voltage can be dangerous or damage equipment.
Figure volts amps watts for water heater
Connect water heater to 120 volt
Connect water heater to generator
Single-phase 208 elements
208 volt as it applies to elements
Elements are called resistance elements.
Any ordinary resistance element can be connected to 208 volts.
For example, connect 208 volt to element rated for 240 volt, and the wattage output is lowered because the element burn cooler than the coil resistance was engineered for.
The lower wattage still heats acceptable amount of water using 208 volts on 240 elements.
If 208 volts is connected to element rated for 120 volt  will burn out element
If 208 volts is connected to element rated for 480 volts, the wattage drops 

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Figure volts amps watts for water heater
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Test element
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Marathon elements
Figure volts amps watts
What is 3-phase?
3-phase is generated at the power plant. It is more efficient than single-phase household voltages, but requires more wiring.
In a single-phase application, there are two wires and each device requires both wires to complete the circuit.
With 3-phase, each circuit requires 3 wires. When power is switched on-off, the switch turns off all three wires.

Consider another perspective that partially explains the difference:
120 volt single phase is like a bicycle without pedal straps. You can only push the pedal downward, and the upward stroke provides no power.
240 volt single phase is like a bicycle with pedal straps, so while one pedal is pushing down, the upward stroke is being lifted. Result: 240 has more power and efficiency than 120.
The limitation with single-phase 120-240 is the lag when pedals are at the top and bottom of the stroke.
3-phase is different.
3-phase is like a 3-legged bicycle with pedal straps (an interesting invention indeed) where the pedals are each 60 apart so one pedal is always in the downward stroke and never are both pedals at the top and bottom at same time. Result the average power is greater.
What is 3-phase: power plant to end user
3U element Three-phase
There are two types of three phase water heaters for commercial application: 3-phase balanced and three phase unbalanced. 3-phase water heaters can be converted to single-phase household voltage.
3U bundle elements are for 3-phase balanced applications and have 3 elements in 1
Wiring uses 3 or 6 wires depending on specification of heater, illustrations shown below.

3U bundle element
3U elements

More about 3-phase water heaters
3 phase elements Three-phase water heater elements
Water heater will specify WYE or Delta
3-phase tankless requires delta (call manufacturer)

3-phase tank-type heater can be connected to wye or delta (call manufacture- look at spec sheet- look at label on side of tank)

6 wire leads:
can be used single phase, or 3-phase delta or 3-phase wye

3 wire leads:
can be used for 3-phase wye only

3-phase water heater manual p17
How to wire 3-phase

3U elements at Amazon

Residential homes in US do not have 208 volt
Residential services have 1 transformer. Inside the transformer are two coils represented by illustrations on left.
The transformer receives 4500-7900 volts from power company on primary side, and the output coil or secondary puts out 120-240 volt power.
Contrast with commercial 3-phase services have 2 or three transformers, each transformer has 2 coils inside.
No matter if the service is 1 transformer or 3 transformers, each transformer has 2 coils inside.
Most residential household electric services are 120-240 volt with 2 hot legs and 1 center-tap neutral. (ground wires not shown connect to center-tap neutral and to the soil.)

Hot leg to neutral gives 120 volt
Hot leg to Hot leg gives 240 volts
208 volts is not available.
Exception: some apartments buildings have 120 and 208 volt that is supplied by the building's 3-phase service.

Illustrations show the primary and secondary coils inside the transformer.
Each transformer consists of primary and secondary coils.
Primary wires are the power lines coming from substation.
Secondary wires connects to lines going into customer's breaker box

See inside main breaker box
Electricity generation: power plant to home
Why you need ground wire

Larger image
Three-phase and single-phase
Some buildings & apartments have 208 volt

208-120 WYE or 208 Delta service
1 hot leg and 1 neutral provide 120V single phase (wye only)
2 hot legs provide 208V single phase, and wiring for 208 volt looks identical to household 240 volt wiring.
3 hot legs provide 208V three phase

Note: the delta configuration does not have neutral connection so 120V is not available

Images show 3 transformers, normally found on the power pole near each business, or located underground in waterproof electrical vault..

How to identify transformer wiring
Transformer resources
How to wire 3-phase

high leg delta
Larger image
Three-phase and single-phase
Commercial buildings with high leg delta service have 208 volt
High leg delta or split-phase Delta service
120-208-240 volts configurations

208 volt is derived from the center-tap neutral and the Hot leg furthest from the center tap.

Illustration shows 3 transformer coils on secondary side, primary coils are not shows.
Each transformer consists of primary and secondary coils.
Primary connects to power lines coming from substation. (not shown)
Secondary connects to wires going into customer's breaker box

Not shown are Open delta and open Wye

How to identify transformer wiring
Transformer resources
How to wire 3-phase
Distribution wiring diagrams
Difference between Delta and Wye
Delta transformer coils are wired in parallel.
WYE transformer coils are wired in series.
Delta has lower amps/ meaning less heat.
For example many transformer banks are wired Delta on the Power company or Primary coils, and Wye on the customer or secondary coils. The reason for this: the primary side voltage can be 4500-7900 volts, and using delta configuration means lower amps which means the manufacturer can use smaller wires on the primary side coils and save money.
Materials used for the power grid are a balance of cost, safety, and function.
Star-Delta (WYE-delta) is also a configuration used for motor starter timers, such as a star-delta timer. With motors, they consume a lot a of amperage to start so the motor is started with the star or wye configuration, and after the motor gets going, the circuit is switched to delta for higher efficiency.
How to identify transformer wiring
How to calculate the voltage for WYE
Test Hot to ground = voltage
Test Hot to Neutral voltage multiplied by √3 (1.7333) = Hot to Hot voltage
Test Hot to Hot voltage divided by √3 = Hot to Neutral voltage
Calculations assume balanced voltage across all three lines

Orange 10 gauge 30 amp breaker

Orange/ #10 gauge for for 30 amp circuits including water heater
with ground
10-2 gauge/ 30 amp
10-3/ 30 amp

NMB is house wiring
UF is underground

Yellow 12 gauge 20 amp breaker

Yellow/ #12 gauge wire for 20 amp
with ground
12-2 gauge/ 20 amp
12-3/ 20 amp

Rolls of stranded wire

NMB is house wiring
UF is underground
White 14 gauge 15 amp breaker

White/ #14 gauge wire for 15 amp
with ground
14-2 gauge/ 15 amp
14-3/ 15 amp

NMB is house wiring
UF is underground

Copper ground wire
Use same size as other wire in circuit

Spools of ground wire
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