The Regeneration is a way to continue to play without catching the yoyo. When your spin has gone down you can perform this trick to give you more spin, though the direction of spin is now opposite. Direction of spin is important to 1A play. If you play against the direction of spin the yoyo is far more likely to catch and come up prematurely.
When the origin of spin comes from a breakaway or trapeze, you are going to get in your bind position then turn your body so that you are in front of the yoyo. Now bind the yoyo and at the last second swing the yoyo forward instead of catching it. That is a regeneration. Keep in mind the direction of spin for the yoyo is now different so you are limited to front style tricks unless you regenerate back into a trapeze or catch the yoyo.
When the origin of spin comes from a front style through you are going to get into your bind position then turn your body so that you are parallel with the yoyo. Perform your bind and at the last second turn your wrist so that you swing the yoyo outward instead of catching it. The yoyo will come around and you can mount a trapeze or any side style mount or trick.
Tricks to know before Basic Regenerations: