I'm not sure about the name of the tool, but it is a little wire brush that you rotate to clean out the primer pocket.
You can buy it with a screwdriver like handle and do it by hand. It works fine, but it gets old quickly.
You can put the brush in an electric drill. That works fine too. When I did it that way, I locked the trigger on the drill at low speed and put the drill in a vice I have on my workbench.
RCBS makes a piece of equipment that will take four rotating tools. Examples are a bevel and champfer that take the burr off of trimmed cases, something that takes the crimp off of primers pockets where the primers were crimped in and the aforementioned primer pocket cleaning brush.
I've tried cleaning and not cleaning the primer pockets and never noticed any difference in whether the round fired or not. Howerver, cleaning them scratches my OCD itch so I do.