RESEARCH: The 180-Degree Rule

The 180-Degree Rule, rather than being a style of editing, is in fact an editing technique designed  to retain the continuity of the scene. A good visual would be the picture below;

The picture here depicts where the camera can and can't film from. The dotted line represents the 'cut-off point', the purple arrows being where you can film from, the red cross where you can't.

If the camera crosses the 'line' then the characters will seem to have switched places, disorientating the viewer and ruining the effect.

The effect is done by imagining a line through the two characters in shot, a semi-circle around them. The camera may film at any point within the semi-circle without ruining the continuity of the shot.
However, if the line is crossed, then the characters will seem to have switched sides, confusing the viewer and thus distracting them from the action.

The only time the line may be breached is if it is done in one continuous take. If done correctly, it will appear the the viewer that the camera has only panned around the characters, and thus the viewer won't be distracted.

The 180-Degree Rule is used to maintain the image of verisimilitude throughout the scene, keeping the continuity. They do not want the audience becoming distracted by the characters seemingly switching places, as they would then break from the plot and possibly feel that the film/television series is poorly made. Thus the rule is instigated to prevent this.

Below is an example of  the rule, as well as how not to do it, and a demonstration of 'crossing the line' when done correctly.