Continuity editing is a system pioneered by early filmmakers to join a series of separate shots into one continuous experience. It seeks to make shots as inconspicuous as possible and to provide enough information for the viewer to fill in the gaps where necessary. Continuity of action is a central tenant, the idea being that a single action is continued across both shots. IE- a man starts to raise his arm before the cut, and in the next shot, we see his hand reach his head. This helps the two feel continuous and decrease attention paid to the cut itself. Eye line match is another important element. This is related to the axis of action, and the importance of having each character associated with a particular side of the screen, especially during dialogue sequences, in order to avoid confusing the viewer in regards to spatial relationships.
If we are used to seeing Bill on the left side of shots in this particular dinner scene, and Brad on the right, then if Bill suddenly appears on the right, it can potentially confuse viewers.
Dramatic rhythm is another important element of continuity editing. The idea is that the pacing of the shots and the pacing of the action are fundamentally important to the way we as viewers perceive a scene. An example would be a well cut fist fight scene, in which the pacing of the shots and the sounds take on an almost musical quality.
Another important idea in continuity editing is that we as viewers follow the eyes of the characters on screen. If we see a character look towards the wall, and then we cut to a clock, we read that as the character looking at a clock.