Each level in the game is divided into sections that are loaded individually as the player crosses specified boundaries called "loading points". Such loading points most recognizable by the split-second lag and the phrase "Loading...Done" that appears on the side of the screen. When a loading point is crossed, the area that the player is leaving appears frozen in time.
The same process happens to all of the actors -- that is, all allies, enemies, NPCs, vehicles, weapons, and really everything that isn't a fixed, static part of the terrain. When you leave an area, all of the actors from that area are also frozen. Their AIs cease to function, and they stop moving -- they don't even fall down when killed (though they can bleed and do drop their weapon). The effect stops if the actors are returned to their original locations.
Obviously, Bungie didn't want players to interact with -- or even see -- such "frozen" actors, and they took steps to prevent such things from occurring. For example, Marines are often programmed to stop moving forward when they are about to reach a loading point (ostensibly so they can watch the Master Chief's back). However, while the game takes steps to prevent actors from leaving their designated areas, it never actually checks if they're still in their designated areas when a loading point is activated.
The glitch, then, is the ability to freeze actors in place beyond their normal areas. If you can, through any means, take any actor -- be it a Marine or even an enemy -- through a loading point, then you can interact with the actor while it is frozen.
Usually the game's design prevents the player from forcibly moving NPCs from one area to another. There are some instances where Warthogs can be used to work around this limitation.
The Silent Cartographer
Play through The Silent Cartographer until you reach the first Forerunner structure. Fight your way inside, and Cortana will advise the Master Chief that he should not allow the Covenant to close the doors.
Once the doors have closed, ferry the Marines that came with you from the drop zone to the room in front of the door, using the Warthogs available on the map. Ensure you bring most, if not all the surviving Marines to this room. You can ask them to disembark from the Warthogs if you wish, but you run the risk of killing them when you bring your next load of Marines with you.
Once you've finished, this room should now be full of Marines, with some on foot and others in Warthogs. At this point, continue with the mission as normal. When you trigger the next cutscene and unlock the door, the Elite Zealot inside will be killed by your Marines almost instantly.
Once you have activated the Silent Cartographer, you will receive a message from the Marines, stating that they are coming under attack at the Landing Zone -- but that is impossible, because they are actually completely safe within the building you are in. On your way out of the Forerunner structure, return to the room you left the Marines in. They will be frozen.
Sometimes, when returning to the Marines, they will all have died for no apparent reason.
Note that the Marines may be taken to the room at any time before you activate its loading point.
Assault on the Control Room
Another such instance is present in the level Assault on the Control Room, at the area where the Master Chief and the Marines fight their way through the deep canyons into a dead-end with the two final bridges high above them. The only way out of the canyon at this point (at least, according to the game's intended design) is through a single small door on the right side of the canyon. The Marines will not follow, instead staying behind to guard the Master Chief's back.
While it is somewhat difficult, a Warthog can, with a little effort, be forced through some pillars and into this area of the canyon. If the player fills the two extra seats with Marines and then forces the Warthog through the door into the corridors, then once the Warthog crosses the loading point the two Marines will freeze. This happens because when the player leaves one area, all the "living" elements in that area, whether NPC, Covenant, vehicle, explosion, etc., are frozen where they are -- and no checks are performed to make sure that the now-frozen objects are where they belong. You can shoot the Marines once they freeze and while they may make sounds, they will not move until you return with them to their specified area. For some reason, Needler rounds and Plasma Grenades also take longer to explode when stuck to frozen Marines -- it can sometimes take as many as three Needler clips before a detonation occurs.
Another example of this glitch can be seen in the same level, in areas where Hunters roam the interior rooms. If you can get one to follow you into a corridor that contains a loading point, once you cross that point, the Hunter will freeze. However, firing into the frozen area or throwing a grenade into it will not freeze that bullet/projectile or grenade. Instead, it will act normally, and if you've damaged the Hunter blood will even splatter on the floor and walls. If you damage it enough while it is frozen, it will die while frozen, but not fall down until you re-enter the frozen area.
A third example of this can be found when you cross the underground canyon. You first have to kill all the enemies with the tank and storm througth the gaint blast doors and a slight distance around to corner. Once done, get out of the tank and run back to the doors. There you will see the frozen Marines. If you go back into the previous zone they will come back alive, however is you continue on instead they will stay frozen besides the fact that they are meant to follow you. Some time's if you keep freezing and un-freezing them they will be stuck that way no matter what you do after.
In Halo 3
The glitch is present, albeit in a slightly altered form, in Halo 3. When a player leaves an area, all elements in that area are frozen. Elements that travel with the player are not frozen, however. The only reason that this is a glitch in Halo 3 is because it can be seen with Theater, when it was likely never intended to be noticed at all.
A simple example is the Campaign level The Ark. If, upon encountering the first pair of Hunters in the level, a player returns to the previous area (where they had to snipe down a Covenant Pack) and then views the resulting Film in Theater, they will find that while they were in the previous area, the Hunters (and everything in that general region) were completely frozen in time.
In that instance, the effect can be quite helpful, as players don't need to worry about their ODST allies being killed if they need to go back for ammo.