From Halopedia, the Halo wiki
Crouch jumping is a technique in which a player crouches directly after jumping. The move brings the player's legs up, reducing their height and allowing them to jump into higher places or smaller gaps. In Halo: Combat Evolved, it could also lower fall damage.
The technique has also been called "duck jumping", "high jumping", and even the "Gandhi jump".
The technique is extremely simple to perform. One needs only to jump, and crouch in midair. This can allow one to reach previously-unreachable places.
As previously mentioned, Crouch jumping is useful for jumping to slightly higher locations or into smaller gaps. It is also an effective technique to use when strafing around an enemy during a firefight. It can be used to help teammates (in Co-op or team Multiplayer games) reach higher places.
The reason this trick works is not because it makes a jump higher: When jumping normally, the place a player is trying to reach is occasionally too high, and their feet will hit the platform edge. This causes them to fall down or simply bounce off the wall. When the player crouch jumps, their hitbox becomes smaller (as it would while crouching), and the edge of the platform stops being an obstruction. Many Carney Holes require some form of crouch jumping, as does the Lonely Soul Easter Egg.
While mid-air, players can crouch and uncrouch repeatedly to gain more air time. Such a move can also, when carrying a one-handed weapon in Halo: Combat Evolved, make a player appear unarmed.
Those that use the Toggle Crouch option may find crouch jumping more difficult, as the transition from a standing form to a crouching form is not as smooth with the setting enabled.