An L cut, also known as a split edit, is a transition from one shot to another, where the picture transition does not occur coincidentally with the audio transition. This is often done to enhance the aesthetics or flow of the film (for example--a conversation between two people can feel like a tennis match without L cuts. L cuts allow the audience to see the reactionary impulse to speak, or the aftermath of speaking rather than simply the act of speaking.) L cuts are also used to hide transitions between scenes.
One example of an l cut in film would be in The Silence of the Lambs, when Jack Crawford is telling Clarice Starling never to forget what Hannibal Lecter is and Clarice asks "And what is that?" The scene cuts to an establishing shot of the "hospital" where Lecter is being detained, while Dr. Frederick Chilton's voice says "Oh, he's a monster." Dr. Chilton then continues a description of Lecter as the visuals cut to him in a closeup.