Polyurethane is a different kind of rubber.
Normal rubber bushings look like this:
They are made of (natural) black rubber vulcanized to an outer (and sometimes inner) metal shell. That shell is most of the times press fitted (so under a press with force) into the component of the car (subframe, chassis etc). To get them out can be a real pain if you don't have the specialized tools.
The black rubber deteriorates over both time and miles. It is not a very stable substance.
The rubber bushings work as a stretch kind of device. The inner (metal) part is connected to (for example) a control arm and the outer part is connected to the chassis. When the control arm moves (like up and down), it flexes the rubber (over and over again)
Polyurethane bushins look like this:
or this:
They are made of a special synthetic rubber (polyurethane), which does not deteriorate over time or by flexing (unless stressed too hard, then it tears).
They are more like a bearing, where 1 part moves and 1 parts is fixed. The inner part is fixed to (for example) the control arm and the outer part to the chassis. Between those parts it has to be lubricated! (It is usually supplied with copper grease). Sometimes people say they can make noise (squeeking); which is obviously the lack of lubrication. When properly lubricated and not stressed to extreme (racing) they last much longer than the stock bushings, and do not change roadhandling over time. The rubber does not age, so it keeps that fresh tight sense of control. You can get them in different stifnesses, where usually the softest stiffness (shore80A) is a little bit stiffer than stock, but not by a great amount.
Usually they are more easy to fit; many designs pop right in by hand.
You can regard them as a performance mod.
from the powerflex site:
http://www.powerflex.co.uk/road-series/why-pu