Ok so - cush rubbers
If your sprocket was bolted solidly to the back wheel, the only form of shock absorbtion in the drive train would be the slack in the chain - very rough. So they bolt the sprocket to a carrier plate, and that is keyed into the back wheel via a set of rubber bushes. Next time you're next to another bike, watch the back sprocket when he puts it into gear - it'll move.
Now you don't want too much movement or you're losing power, and soft rubbers are nearly as bad as no rubbers at all. To see if they are worn out, hold the sprocket at a quarter to three and try and move it like a steering wheel - anything more than a couple of mm, or if you can feel free play, and the rubbers want replacing. A good test when you've got the wheel off is how easy does the carrier plate fit back into the wheel. If you have to stamp on it then they're ok. If it falls in they're shagged.
If you can rock the sprocket and carrier plate then the inner bearing is probably shot. These seem to wear fairly quickly as you use a lot of soap and water round there to clean off chain gunge. Easy job. Check the bearing number and buy a new 'un. Pop it into the freezer overnight. Then stick the carrier plate into the oven at 120 deg C for 10 minutes. Hammer old bearing out and pop new one in