Frozen Elite refers to three separate glitches in two of the Halo games. The first glitch causes a live Elite to freeze in place in Halo: Combat Evolved's Campaign level Pillar of Autumn; the second can cause Elite corpses to freeze in midair. The third glitch causes an Elite's corpse to freeze in an odd position in Halo 3's campaign level, Cortana.
Halo: Combat Evolved
On the Pillar of Autumn, when the player is going to the bridge and they run into an Elite, there are some Marines shooting at him. Lead him through the door toward the Marines and he will freeze. The player can walk through him and the Marines won't shoot the Elite, but if they attack him, it will sound like they hit a solid body.
Also, when playing some other levels on Co-op, if one person kills an Elite at the same time that the other person hits a checkpoint, the Elite will sometimes freeze while falling (The margin of error for this is less than a second).
A frozen Elite corpse can be seen in Cortana, in the infested High Charity. As the player travels through the level, they'll find an Elite's corpse sticking out of the ground at an oblique angle. He is clearly dead, and can only be unfrozen by hitting or shooting him. This glitch happens because the Elite is partially inside of the immovable ground, effectively locking its body in place.