The longer answer
A shotgun pellet takes time to travel from the muzzle to its target. At trap distances — roughly 32 to 46 yards — that flight time is between about 100 and 150 milliseconds. The target, meanwhile, is moving. If the gun points directly at the clay at the instant the trigger breaks, the pellets will arrive at the spot where the clay used to be. The shooter has to lead it.
How much lead depends on three things: how fast the clay is moving across the shooter's line of sight, how far away it is, and the speed of the shells. A clay crossing at a 90° angle at 30 yards needs more lead than the same clay at 20 yards on the same heading. A clay flying directly away needs almost none.
Three methods
Three classical techniques produce the same outcome by different paths. Most shooters end up using all three at different moments without consciously switching between them.
Sustained lead. The barrel moves with the target, holding a constant gap in front of it. The trigger breaks when the gap looks right. Predictable, repeatable, and the easiest of the three to teach to a new shooter.
Swing-through. The barrel starts behind the target, accelerates through it, and the trigger breaks as the barrel passes through the clay — the gun's continued swing producing the lead naturally. Natural for fast crossers; harder to coach because the timing lives in the shooter's reflexes rather than in a visible gap.
Pull-away. The barrel matches the target's speed first, then accelerates away from it just before the shot. A hybrid that handles targets whose speed changes mid-flight — a quartering bird that flattens out, for example.
Pick one as your primary and become fluent in it before chasing the others — depth in a single method buys more broken targets than a shallow grasp of all three.