I thought he was talking about cooling the wires using water to reduce the heat generated.
Theoretically yes, it would provided an advantage but it would be painfully small for most home electronics. You'd have to have a next to 100% free supply of water to make it worthwhile.
High power electronics IS water cooled. However, at least 50% of the cooling is purely because without it the equipment would overheat and fail. The other 50% is probably because the equipment becomes very inefficient or distorted at elevated temperatures.
The problem with cooling normal copper wire is that it will always have some level of resistance, and you need to cool it quite a lot to lower it much. So to keep it at the same temperature you'll always have to have the correct temperature water flowing over it.
If, on the otherhand, you were using superconducting wire, it would definately be worth cooling it down since it's resistance does a vertical nose dive down to zero once it gets to a certain temperature. Once you reach that temperature, the wire will no longer warm up the coolant. It'll still get warmed up by the less than perfect thermal insulation around the pipe, as the copper wire example would, but it's one less source of temperature variance.
If you were designing a high power radiotransmitter or a laser for use in fusion experiments, water cooled wires would be realistic.
In fact, a normal desktop computer is an example of a conductor that needs cooling. Without the fan running over your CPU, the heat generated by the resistance could toast the processor in not much more than a few seconds - most computers will automatically power down if the fan stops or they sense the core temperature rise above a set point (mine sounds an alarm at a temperature point a few degrees below the shutdown temperature).
Supercomputers often use liquid to cool the processors since there'll be thousands packed into quite a small space.
Another example would be a hairdryer or electric space heater. One way to look at it is that the element is warming the air flowing over it. Another way is that the air is cooling the element, which will burn out if turned on without the cooling fan.
In short, if you're putting huge amounts of current through a less than perfect conductor it'll probably need cooling. As it will if you're putting less through a conductor with a really high resistance.
As for current and voltage, the two are tied together by power. I can make 10W by having 1A at 10V or 10A at 1V (or any other combination that multiplies together to make 10). In real life, a lot of equipment wants a specific voltage and current to achieve a certain power rating (not anything that multiplies to the same rating) because the materials the equipment is made out of, as well as how it's laid out inside, set a preference for the balance of voltage and current that's sent through them - so they'll only let you reach so many watts of power if you supply it in the volts / amps form that's best for them.
An example is a lightbulb compared to a computer's CPU. Both a lightbulb and a CPU draw somewhat similar amounts of power. A lightbulb will work from the 240V mains and draws quite a small current to create that power. A CPU on the other hand converts the 240V down to just a few volts and supplies the core with lots and lots of amps to create a similar amount of power. The core has very little resistance, so it only needs a low voltage to move lots of electrons through it. If you plugged the core of your computer into the mains, it'd magically transform into a piece of worthless junk in the blink of an eye. Similarly, a lightbulb wouldn't light up anywhere near as brightly if run from the computer's low voltage / high current power supply - the low voltage wouldn't be enough to 'push / pull' the electrons through the higher resistance element, just because the supply can give out a high current, it doesn't mean it will if it's connected to a high resistance and can only put a low voltage across it.
I think of electricity like water. The current, in a circuit is like the drops of water in a stream... it's how MUCH water is there. But water doesn't go anywhere without a reason, it just sits in a puddle. The voltage is like the slope the stream is running down, it's how FORCEFUL the water is. Resistance is like putting a big paddle wheel in the stream. And the power is like how much work I can do with the torque from the paddle wheel, inside my mill grinding flour. If I have a huge river, if it's barely flowing it'll just trickle past the paddle wheel slowly. If I had a small stream that was coming down a nearly vertical slope, it'd push through the wheel quite quickly - but since there isn't so much of it, I'd still only be able to grind roughly the same amount of flour.
To grind more flour I need to keep the stream the same size, or bigger, and the speed it's moving the same of faster - one of those, or both, needs to get bigger.
My water example works for quite a lot of other electrical properties as well, like capacitance. It fits quite well.
If you've ever thought about gas or liquid flow through pipes, as someone else has pointed out, you loose flow rate and pressure in real world pipes because the water has to drag along the pipe walls, which slows the water down. You can replace my paddle wheel example with the pipe example depending on how you're feeling.
As has also been pointed out, the static and dynamic friction in the pipe idea doesn't quite apply to electrons so well. Although, the impulse of accelerating an object could be likend to the magnetic induction that occurs as electrons start to flow or need to change direction. That's pretty complex stuff if you're new to electronics though.
A blistering number of people don't know the difference between amps and volts or what power is. So once you get it, you're in quite a small minority.