Definition of flat call
A flat call is the act of simply calling a bet when a raise is possible. In this situation, you are sandwiched between two players. For example, you are on the flop in button position. There are three players on this flop with the UTG player and the SB. On the flop, the small blind checks, the player in UTG position bets and you call. Here your play will be defined as a flat call since the action is not over. The small blind is still in the hand and could raise (check-raise).
The symbolism of the flat call
What does a flat call mean? Obviously, it depends on your skill level, but when a good player flattens, it means he is very strong. It is difficult to make a flat call unless you are very strong. You'll see some fishes make flat calls while being weak, but good players will do it while being strong. For example, imagine the following hand: UTG raises preflop, UTG+1 3bets and you make a flat call on the button. Here, UTG could very well go for a 4bet. The players have an uncapped range. For this reason, your flat call will show a lot of strength.