We've got two main characters in The Shawshank Redemption, and one of them does double-duty, playing the part of our narrator. Half the time he's engaging in dialogue with the other characters; the other half the time he's giving us the lowdown on the down-low.
It's important to get our information through Red because, well, Andy doesn't say too much. Since our protagonist is such a quiet, introspective soul, it helps to hear his close friend tell us what he's thinking, or what he might be going through. Of course, he also catches us up on some stuff we don't get to see much of, like how Andy came to be in Shawshank in the first place.
Shucks, though. It's not like we don't care about Red, too. Fortunately, we get to hear plenty about what's zipping around in his head as well. It's actually pretty common that a film based on a book will use this technique, because in books, much more than in movies, an author has a chance to provide a window into the characters' innermost thoughts and desires in addition to just the surface actions and events. There's a lot to cover, so it's nice to have a narrator who can communicate some of that deep stuff to us and keep the movie from being 4 hours long.
Shawshank also makes generous use of montage, which serves the dual purpose of informing us what certain characters have experienced while using up minimal screen time (like when Andy is being abused by Bogs and his boys, or when Brooks tries to adjust to life on the outside), as well as creating the illusion that there's a large passage of time—in this instance, twenty years.