If you're not sure what a superconductor is, basically anything that conducts electricity has resistance in it.
That resistance turns the energy that is being transmitted through the conductor into heat, essentially wasting it for useful purposes unless you're running a hair dryer or oven.
For instance, one of the reasons why power plants have to be near the cities they serve, aside from practical logistics, is that if you send electricity over power lines, you lose some of that electricity to the resistant line drop, the voltage decreases over time, and ultimately you could lose all of your usable power to heat.
However, that changes when superconductors come into play. Many power plants already use them for short distances where the heat is high and the line drop is also high, but if you replaced every power line in America with superconducting lines a power plant in Florida could sell extra spare power to Alaska with no loss between the two plants. (This is in theory, it is still likely that there would be losses where the lines are split and connected, but that would still be far less than the greater than 100% voltage loss over 7,000 miles of traditional copper lines that you would expect.)
Room temperature superconductors would provide many benefits aside from power transmission as well. Electric vehicles would be more efficient with power coils made from them, allowing more of the electricity from the batteries to be turned directly into vehicle movement.
Cell phones would heat up less with superconducting wires, losing less of their battery power to heat and lasting longer.
Computers would run longer. CPUs would heat up less, requiring less cooling to operate at higher speeds and less power to run closer to the atomic limit of processing.
If it is proven that this works, then we may be very close to the system by which superconductivity works, and solving that may allow for hundreds or thousands of compounds exhibiting superconductivity to be made for myriad applications, allowing for us to live closer to the way we tend to while being a bit greener in the process.
