This is model error acheived by exploiting a glitch in Halo 2. It allows one to separate the character's upper and lower body.
To do this, simply look down, at your feet, and spin around. If your look sensitivity is high enough, you will notice your torso spins faster than your lower body, and you can in fact turn your torso 360 degrees more than your legs. This does not affect your health and can be acheived playing as either The Arbiter or John-117.
Methods
Object bump method
On the level Gravemind, when you are in the Mausoleum of the Arbiter, walk up to the Arbiter's armor sarcophagus, and try to walk inside through the front, where the Arbiter got his armor out from in the Sacred Icon cutscene. Look down while you are doing this, and John's legs will be completely separated from his torso.
Scarab Method
Another method for this glitch is on Metropolis, play until you reach the part where you jump onto the scarab from the bridge. Jump onto it and then wait until it stops.
After it stops, go onto the right or left back leg of the Scarab. Walk into the body of the Scarab and move back a little.
Look down to see your legs moving without you.
This is basically the same with The Great Journey except you must fly onto the Scarab in a Banshee. Fly with the Banshee onto it.
Scorpion Method
First, you must get the Scorpion onto a sharp incline, such as the rails opposite the bases in Waterworks, or between an edge and the ground. You must tilt it so that the cannon is facing upward.
Second, get onto the body of the Scorpion. Walk under the cannon, crouching, until you see a cross-section of the cannon. If done right, your legs will walk out from under you and keep moving so as to walk forward, but they are stopped by the joint between the body and the cannon of the Scorpion.
Halo 3 Cold Storage Method
On the Halo 3 multiplayer map Cold Storage, find the yellow tube with the flood tank form inside of it. In forge mode, place a machine gun turret directly in front of the tube so the back of the turret is inside of the tube. Get onto the turret and look up. Then turn into the monitor. This should get you inside of the tube. Now turn back into a Spartan/Elite. Now look down and sometimes you will be able to see the bottom half of yourself.
Why it happens
When Bungie modeled the characters in the game, they modeled the two halves separately to make it easier to animate turning without moving your legs. This results in some unintentional separation because of the shape of some of the game's geometry.