Let's first consider the case with the discount factor $\rho = 1$.
In any finitely repeated case, the NE is to play (cheat, cheat) simply because of backward induction. A sophisticated rational player would think that, in the last round, the other player has no chance to punish him by playing cheat in the next round because there's no next round, therefore, he will play cheat. Another sophisticated player of course can also anticipate this and play cheat also in the last round. Given this, in the second-last round, no player can punish the other one by playing cheat in the next round because they are both playing cheat in the next round, and thus, they will both play cheat in the second last round. The same process goes on and on until the first round, and both players will also play cheat. The key thing here is there is a last round to begin with in a finitely repeated case.
In the infinitely repeated case, there is no last round to begin with, so each player can punish the other player by playing cheat in the next round if the other player plays cheat in this round. The presence of punishment makes the "tit-for-tat" strategy become an equilibrium in this case.
However, when the discount factor $\rho$ is sufficiently small, the "tit-for-tat" strategy can not be an equilibrium any more. The discount factor $\rho$ is usually interpreted as how much one discounts future utility. In an infinitely repeated game, $\rho$ can also be interpreted as how likely one player is going to play the same game with the other player in the next round. And straightforwardly, the less likely they are going to interact again, the less credible the threat is of playing cheat in the next round.
PS: I previously thought the TfT strategy was the Grim strategy. Thanks to @VARulle for pointing this out.