Parallel editing is a technique used to portray multiple lines of action, occurring in different places, simultaneously. In most but not all cases of this technique, these lines of action are occurring at the same time. These different sequences of events are shown simultaneously because there is usually some type of connection between them. This connection is either understood by the audience throughout the sequence, or will be revealed later on in the movie. The first clip is from No Country For Old Men directed by the Coen Brothers, and the second is from Batman: The Dark Knight directed by Christopher Nolan.
Further explanation and videoclips behind the cut