Betting River, Folding to a Raise

[Frond]

This is geared with LHE in mind. What is the actual theory behind this?

Say you have a hand like top pair with a weak kicker, you have bet along the way and got called by 2-3 players. Now it is the river. Your'e first to act. Sometimes I read people's advice of: "bet river, fold to a raise". I know it is a vague question and I didn't give a lot of specifics, but why take the bet/fold to a raise line instead of C/C or C/F? I know depends what what is the general reasoning behind this. If you are not sure where your'e at, why not check call for a bet instead of betting,facing a raise and having it cost you a total of 2 bets to showdown?