Crouch jumping

The Crouch Jump, also called "Duck Jump", or "High Jump", is a technique where one first jumps and then crouches in mid-air. This will bring up your legs and, for some unknown reason, your entire body, allowing a little more height to reach higher places, such as better sniping positions. Also, when you fall from heights that would normally kill you, if you manage to crouch while falling, you may survive.

Background
In Halo 2 and Halo 3, however, the damage reduction for the crouch jump is unnecessary due to the lack of fall damage. In addition, if the fall is too long, then even a crouch jump won't save you. For example, if you jump off the bridge on Gephyrophobia, you will not make it, despite your crouch jump, because of the extreme height of the jump and also because of fall timer. Crouch Jumping is also very useful for performing Tactical Jump and helping fellow players (in campaign or team multiplayer games) reach higher places for protection or tactical advantages.

Performing The Jump
The method of crouch jumping is relatively simple. Press 'A' to jump and, while in mid-air, hold down the left thumbstick to crouch. This should enable you to get to previous unreachable places. The reason this trick works is not because it makes you jump higher. What actually happens is that when you do a normal jump, occasionally the place you're trying to jump to is too high and your feet will hit the platform edge, thereby not allowing you to get to where you were trying to go. When you crouch jump, your hitbox becomes smaller, as it would while crouching, allowing you to gain extra vertical clearance, something incredibly valuable when it comes to reaching previous inaccessible areas. Many Carney Holes require some form of crouch jumping.

You can also, while mid-air, hit crouch repeatedly to gain more air time, but not necessarily more height. It also seems in Halo: Combat Evolved, that with a one handed weapon (like a Plasma Pistol or Pistol), you will look like you are jumping with no weapon to another player (arms apart).

In Halo 3, with the addition of the toggle crouch option, crouch jumping has become a somewhat harder task to do, at least for those who use toggle crouch, due to the fact that its transition from standing form to crouching form is not as smooth as the default style.