[NohatCoder]

The kite goes sideways relative to the wind, spooling out the tether, generating power, and speeding up. Just like a high-speed sailing boat it can reach several times the speed of the wind this way. Then when time comes the kite turns into the wind, letting the tether spool back in at no real energy cost (but not generating power during this period). The kite then turns again to repeat the process.

Note that while there are several different techniques, they all rely on the kite moving fast, this allows it to sweep a large area relative to its size, thus working around the fundamental limit that you can't extract more energy than some percentage of the directed kinetic energy contained in the air molecules moving through the swept area.