Pre-lap

A Pre-lap is a scene transition where the sound from the scene transitions before the visuals do, so the sound of the second scene momentarily coincides with the visuals from the first scene.

Because the viewer will naturally try to connect what they are seeing with what they are hearing, it is often used to portray a logical connection between the two scenes.

This is also sometimes employed in comics by including speech from one scene as narration boxes over the preceding scene.

The reverse of this is the Post-lap.

Film

 * The Graduate, where Dustin Hoffman is in the bottom of a pool but you hear him having a phone conversation with Mrs. Robinson in the following scene.
 * Indiana Jones and the Last Crusade. As Indy is looking at a road sign leading to Berlin, the sound of drums is heard. As the scene changes to Berlin, the drums fade into parade music as Nazi soldiers march around and burn books.
 * An interesting one in Star Wars Episode I: When Shmi overhears Qui-Gon discussing the implications of Anakin's impossibly high midi-chlorian count, Darth Maul's Sith chanting theme begins, serving as a lampshade on the conversation before transitioning to Maul's arrival.
 * Lawrence of Arabia, where the sound of a train whistle is heard over the end of the previous scene. The Ur Example and Trope Maker.
 * Primer has a scene in which an ice machine is activated on a refrigerator, and a noise is heard. Said noise turns out to be construction equipment from the next scene, where the protagonists are trying to build a device in the garage.
 * Rather bizarrely, considering the lowbrow humor of most of the movie, Scary Movie 3 actually directly parodies this rarely-noticed-or-discussed phenomenon during its parody of The Ring, with the main character reacting to a sudden boat horn piped in from the next scene. Not sure anybody else got it.

Live Action TV

 * Constantly used in Eastenders.
 * Lost used it often, particularly for transitioning to flashbacks in the early episodes, before the trademark "woosh" noise was added.