Originally Posted by hutz
Umm, I think OP was refering to min-betting, not necessarily min-raising.
You are correct. OP did say min-betting, not min-raising. My mistake. Again, I can only speculate, as this is not something that I do.
As someone stated earlier, it might be a way of trying to find out where they are in a hand, especially if the flop is in villain's perceived range. Theortically the villain should come over the top with a raise if they have connected. The problem with this is that bingo players are often very passive, electing to call and see cards as cheaply as possible, often waiting to see the entire board before betting out or raising on their own.
Another reason one might min-bet post flop is to start culling players out of the hand when several player have seen the flop. The ones that missed the flop might consider folding, leaving only the players who have connected or have strong drawing hands. If they can narrow it down to one or two players in the pot, then they might be able to start trying to put their opponents on a hand.
I have also seen players do this to trap when they have flopped something very strong, like a set. A min-bet tends to look like a feeler bet, and might induce a raise. If not, it might not be enough to scare other players out of the pot, who might be willing to call with overcards as long the price is cheap. This can build up decent sized little pot when multiple opponents are involved, or just get a little extra value out of a single opponent that might not be willing to call a larger bet.