I saw this several times in different movies, but I don't understand what is this supposed to mean. The main idea is when the scene is about to change, for one second or so we still see the picture from the old scene, but the sound is already coming from from the upcoming scene. Why do they do this? What's the purpose of this technique?
In short one have J-Cut and L-Cut
It can advance the story in itself by moving the viewer ahead. It also can give a smoother transition, or many other effects.
Find the two examples in the article by Chrisopher to be nice examples.
For example in second video, the packing of the cigarette packet is smoothed out by the J-Cut, rather nicely.