The Geometry of a Screen
A screen is a legal obstruction. The screener establishes a position in the path the on-ball defender needs to travel, and the ball handler moves so that the defender's shortest route passes through an occupied space. The handler is moving with intent while the defender is reacting, which means the defender arrives late by however long it takes to go around the obstacle. That gap is the entire mechanism.
What makes the action powerful is that the gap cannot be closed by the beaten defender alone. Somebody has to cover for him, and the only defender close enough is the one guarding the screener. The instant that defender engages the ball, the screener becomes a free attacker moving toward the basket. Two defenders are now responsible for two live threats moving in different directions, one of whom has the ball, and they have a fraction of a second to agree on who takes which. Every coverage in basketball is an attempt to pre-agree that answer so it does not have to be improvised.