A cutback should be used if you are entering a flat section, where the wave is backing-off. Continuing down the line will result in a loss of speed, but a good quality cutback will maintain speed while returning you back to the more powerful part of the wave. When done properly, a cutback can look amazing. This is a technical move, requiring plenty of practice, and commitment, and practice. Also, let's not forget you'll need lots and lots of practice. (are you getting this!)
If it's possible, learn a cutback on a mellow point break or reef. Somewhere where you know that the wall is definitely going to stay up and not close on you.
You'll start the manoeuver when you are moving away from the curl, heading down the line. Make your bottom turn and try to keep plenty of speed, driving up the face of the wave. When you are in a position to make the turn, shift your weight more to equally to the front foot. Look back towards the whitewater, and keep looking in the direction you want to head.
Compress you body, making a T-position with you arms. You'll need to stay compressed though the 180° turn. Turn your arms, hips and torso in the direction of turn, and apply pressure on the back foot. At the same time, shift weight to the bottom rail (frontside - heel down / backside - toe down). Really commit to making a solid turn, and use your front foot to guide the board through the turn. If you don't rotate the trunk of your body, the cutback will lack power and it won't wrap around to the pocket. Feel free to touch the face of the wave as you turn, it's something you'll see many surfers do. (It will also make you look waaaay more stylish!)
Now the turn is complete. You can choose to simply pivot on your back foot, turning back down the line. Alternatively, lift the nose of the board out above the whitewater, and use the force of the whitewater to rebound you back into the wave. The choice is yours.
Watching other surfers can really help you visualise this manoeuver. Here we've knocked together a a video example of both a frontside and backside cutback, featuring Taj Burrow (fs) and Peter Mendia (bs). Both surfers end the cutback in a different way.