Cute Face is a move in which the user makes a cute face and stops the opponent from attacking for some time. It can only be done by Baby Pokemon. Then a screen comes up saying "The opponent is unable to attack!" It only works until the user attacks, unless it attacks with Cute Face, which makes the opponent unable to attack for as many turns as the number of times Cute Face was used. This is why adult Pokemon can't use this, and also because they're too old. This is usually a baby Pokemon's most useful move.
ALL BABY POKEMON CAN USE THIS MOVE.