Ledge jumping, also known as late jumping or long jumping, is a technique present in Halo 3 that allows a player to jump farther. This is considered a form of Trick Jumping, an activity in which players string together useful and creative jumps through the use of glitches and manipulations of the Halo physics engine.
Run over an edge without stopping. Rather than jumping just at the edge, wait a fraction of a second, then jump and continue moving forward. You should jump just after falling off the edge. This is particularly useful around ramps in The Pit, where normally you would jump off a ledge, just miss another ledge or ramp, and have to jump again or go back to a ramp.