In film, split screen is the combination of two actions filmed separately by copying them onto the same negative-- the usual way, for example, of having an actor talk to himself in a dual role. The actor is filmed as he stands at the left of the frame facing right. Then he's filmed standing at the right and facing the other way. The negative of the first action is placed into a printer and copied onto another negative ("the composite"), but this other negative is masked so that only the left part of the original picture is copied. Then the composite is rewound and the negative of the second action is copied onto the right side of each frame. On this second pass, the left side is masked to prevent double exposure.
Sometimes the technique is used to show actions occurring simultaneously--Time Code is a recent example, where the combination is done electronically. Earlier examples, which used printers, include Le Mans, The Boston Strangler, and Woodstock.