Necron is correct. In a lot of games, what they'll do is create a separate object which follows the player at a certain speed, camera will lock onto that object instead. Once it gets really close to the player, that speed also slows down a lot so you get much smoother transitions. One lazy implementation is to have the camera move 1/2 the distance towards the player from where it currently is per step (or similar).
You end up with a camera that trails behind the player if it moves really fast, while simultaneously it won't move much if they stay within the same area and jerk around a lot. I think a lot of tutorials have referred to this as "Smooth Camera".