In Lessons in the Fundamentals of Go Kageyama refers to the snapback as the "brilliant dawn tesuji". Indeed, it is often the first recognizable tesuji for many beginners. The snapback is all about liberties. Specifically, when a captured stone does not provide extra liberties for the capturing group.
Here is a problem that will walk you through a simple snapback example. The key factor is the shortage of liberties. Look for similar situations in your own games. Pulling off a snapback is always satisfying. :D