Alright, this is definitely a weird one. You play a policeman 'driving' through town on a unicycle, with a blue rotating light attached to his helmet. Your only weapon is a truncheon which can be thrown either straight or up. Don't worry, it always comes back like a boomerang.
As every good policeman, you're fighting crime. There are basically two kinds of crimes (enemies). First, there are bank robbers. Their ingenious plan is usually to attach the loot to balloons and thus let it fly away. An aimed throw can pop those balloons (awarding you with points). What makes those bank robber especially nasty is that they're constantly throwing bombs at you, though. Ultimately, you have no choice but to whack them, pick them up while they're unconcious and deliver them to the next passing police car (more points).
The second type of criminal is the punks. As you've learned in law enforcement school, you know what such people deserve: a good beating with your trusty truncheon! They're just asking for it just by being alive (as they don't seem to be doing anything illegal per se...)! More points for you.
Once you get over the initial attraction due to the... original setting, P.C. Fuzz turns out not to be such a great game. It's very limited, nothing new ever seems to happen. And even what's there isn't that good. Why can't the player throw the truncheon backwards, for example? Especially the bank robbers just seem to stay behind you forever, so you don't have a chance of getting them. Also, the pseudo-3D perspective (you can drive a little 'lower' or 'higher' on the screen) doesn't really work. If when it looks as if you've evaded an approaching bomb, you're hit quite often, losing yet another life. The jumping function is pretty much useless anyway.
If you keep in mind that back when this game was released, there was a huge low-price market filled with extremely simple games, it's ok - definitely worth a look for the sake of the portrayal of the police alone, and it also doesn't look too shabby.