Electronic – Alternating Voltage

Current or anything else energy-carrying doesn't need to "get anywhere" long term to deliver energy. Think of how pistons work in a gasoline engine. They only go back and forth and don't "go anywhere" yet still deliver power to elsewhere (the crank shaft).

Alternating current is a bit like the pistons. You can still extract useful work from it.

Another way to look at alternating current is instantaneous direct current that happens to change over time. Let's say the current if following a sine function with a peak amplitude of 1.41 A. At any point in the cycle there is some amount of instantaneous current flowing, which is anywhere from -1.41 A to +1.41 A. Sometimes the current is 0 and you can't get any work from it. Other times it is non-zero and you can. If you break the cycle up into lots and lots of instantaneous snapshots, you can find the equivalent average steady current level you could extract the same work from. That is the RMS (Root Mean Square) value, which in this case is 1 A. At any one time you might get a bit more or a bit less, but averaged over a cycle this AC current will be equivalent to 1 A DC for the purpose of extracting work. This averaging of the instantaneous snapshots is really the integral. You can write it down yourself and see the result. Keep in mind that the work a current can do is proportional to the square of that current, which is why the negative parts don't cancel the positive parts.

From Wiki:

Transmission loss

The advantage of AC for distributing power over a distance is due to the ease of changing voltages using a transformer. Available electric power is the product of current × voltage at the load. For a given amount of power, a low voltage requires a higher current and a higher voltage requires a lower current. Since metal conducting wires have an almost fixed electrical resistance, some power will be wasted as heat in the wires. This power loss is given by Joule's first law and is proportional to the square of the current. Thus, if the overall transmitted power is the same, and given the constraints of practical conductor sizes, high-current, low-voltage transmissions will suffer a much greater power loss than low-current, high-voltage ones. This holds whether DC or AC is used.

Converting DC power from one voltage to another requires a large spinning rotary converter or motor-generator set, which was difficult, expensive, inefficient, and required maintenance, whereas with AC the voltage can be changed with simple and efficient transformers that have no moving parts and require very little maintenance. This was the key to the success of the AC system. Modern transmission grids regularly use AC voltages up to 765,000 volts.