Definition of overbet
A overbet is a bet that is larger than the size of the pot. If you bet €15 on the flop in a €overbet pot, you've made a overbet. We talk about overbet only after the flop and almost never preflop. Even if a player open raise to 48 big blinds preflop, we won't really talk about a overbet. The overbet is identified by the size of the pot. It is mostly used by good players for a variety of reasons.
Reasons to make a overbet
You can overbet for a very large number of reasons. You can overbet with a very good hand, you can overbet for bluffing, you can overbet for merging your range, etc. Let's say you're on the river and the river card completes the flush. Here you suspect your opponent has a pair at most. You have nothing. If you bet normally, you're afraid that he'll call the bet without asking too many questions. If you roll a overbet, you make him think and perhaps discourage him from calling the bet. Another good reason for a overbet is if you have nuts on the river and you suspect your opponent has a very strong hand. Here, even if you make a overbet, you know he's going to call, which will maximize your profits.