Glitches

Glitches are either errors or bugs in any program (game, software, etc) that can cause undesired or interesting results. In relation to Halo, glitches can be exploited in many ways to make the game interesting or annoying.

Halo: Combat Evolved Examples
Not many were present in Halo: Combat Evolved, however there was the occasional glitch that allowed you to ride a Pelican, skip a certain amount of a level, or get out of a map. There is also a guy that copies himself when dead. Also, there is a glitch in the end of the level 'Halo' in which the final structure has marines and two technicians, and if you kill the marines, the techs will curl into fetal position, and if you stick one with a plasma grenade while in fetal position, they will stand up,spread their arms, drop their weapon and start spinning, before being killed by the grenade.

Halo 2 Examples
In Halo 2, many glitches resulted from unforeseen actions the developers did not think could occur. Players could do things such as Super Jumping or Super Bouncing, get past Invisible Walls to get out of maps, etc. "Button combos" also existed, such as one that would allow you to kill a player instantly.

Halo 3 Examples
Halo 3 has been greatly combed over for glitches by a considerable amount of players, but Bungie has put way too much effort into making sure that there are few, if any, in Halo 3. There are a few that do exist in active gameplay though, such as the Mine Glitches, floating objects, driving an AA Wraith, fusion coil glitches, making elephants fly, and the Elephant speed boost.

