One common practice in firearms training is to scan and assess after finishing a firing string. The purpose is to break tunnel vision after focusing on the target, and to maintain awareness of your surroundings. This is a good idea, but in practice it's sometimes done in a way that's less than optimal.
A lot of people swivel their heads to the left and right really fast. The problem with this is that if you turn your head that fast, it's hard to actually see anything. It would be better to turn your head relatively slowly, enough that you can pick out distinct details. If you actually can see things while moving your head that fast, that's fine, but make sure you can. It's good to try to actually pick something to the side of or behind you that you see and take note of, just to force yourself to look for real.
Another common practice is to only look left and right. It would be better to make sure to look behind you as well.
There's also some small controversy over whether or not the muzzle should move with your eyes. I think that obviously if you're going to look to your sides or behind you, you can't keep the muzzle pointed in those directions, so it's better to keep it simple and keep the gun pointed at the original target or straight down while you look.