The screen is set and the ball handler goes the other way. He reads that his defender has already leaned toward the screen, plants, and attacks the side the defender just vacated.
Why coaches use it
It is not a separate play. It is permission. Once your handler is allowed to reject, every ball screen you run becomes two actions, and the defense has to honor both.
It is the natural answer to three specific things. A defender going under the screen is stepping toward the screen before the ball moves, so the drive away from it beats him. A defender fighting hard over the top has his weight going in one direction. And an ICE that jumps early to the high side has committed to the sideline, so the middle is open behind him.
The screener has a job on a reject. He should not stand there. Most teams have him slip back toward the rim or re-space, because two players in the same gap kills the drive you just created.
How it is guarded
The on-ball defender has to stay square as long as he can and not commit to the screen until the handler does. That is easy to say and hard to do at speed, which is why the reject keeps working.
Behind him, the help has to be honest. If the low man and the nail defender are both shading toward the screen side, the reject drive arrives at the rim with nobody home.
If an opponent rejects you all night, the usual adjustment is to go over every screen and live with the drive, so at least the defender is on the right side of the ball.