Soundbites are one or two line clips of spoken dialogue taken from the film, used as an easy way of summing up characters and genre. As opposed to captions or voiceovers, soundbites are in effect, 'straight from the horses mouth'. They are taken from the film itself and serve the same purpose for a dialogue/character based film as showing a plane exploding would for an action film. In terms of storyline, the editing together of a series of soundbites constructs a mini-narrative usually in an order similar to the film's. The most important plot points can be boiled down into a few lines in order to inform the viewer.
When constructing a trailer one of the most obvious ways of giving an audience a taste of the film is to include clips from it. In films where action sequences and special effects are the main selling point these clips will simply be images cut to music. But in a film where character and dialogue are what is important, most notably in dramas and comedies, these clips will come in the form of soundbites.
A soundbite is usually the most effective method of ending a trailer. After the music has come to a crescendo and stopped, the title page has come up and the trailer seems to be at an end there will be one more line spoken that sums up the film.
Watch this trailer for Jane Campion's 1997 period drama The Portrait of a Lady and notice how there are no outside voiceovers, only soundbites that follow a narrative flow in keeping with the film's.

"Unfortunately, no-one can be told what the Matrix is. You have to see it for yourself." - The Matrix

"This tape will self destruct in 5 seconds" - Mission Impossible