It serves to fill in events in the story that the director doesn't want to depict on screen; it helps to describe how a character feels about events shown in the scene, or remind viewers that they are currently watching a flashback; it also has been used successfully to explain away absurd holes in the plot that would otherwise ruin the movie.
The voice over (VO) is particularly popular in US cinema and somewhat less so in British and Japanese; non-US movies that are conscious imitating Hollywood cliches will usually use it as well.
Usually, artistic movies made outside the English-speaking world tend to avoid using the VO because it's a non-traditional narrative technique, and it looks lazy. A good screenwriter doesn't need to use it. However, in commercials and TV "journalism" it is almost supernaturally powerful in persuading people of utter nonsense; it's basically a form of posthypnotic suggestion.