Well, I need to sleep, so I suppose it's time for more filler, eh?
Speaker surrounds are the bits of flexible material that join the cone - the part of a speaker that makes noise - to the frame. They must be flexible to a precise degree, as the resistance of a surround can make a huge difference to how a driver performs.
While not so common today, several varieties of foam rubber were very popular for use as surrounds, and could be found on almost all speakers, from the worst to the best. As opposed to earlier solid-rubber and cloth surrounds, they were much less resistive, and were far superior sonically.
The problem is, though, that these foam surrounds degraded quickly, and as a result many fine old speakers are useless because the surrounds are gone. Without a surround, the driver no longer is usable, and a perfectly good speaker goes to waste.
However, so long as the rest of the speaker has not been damaged by rubbing, the driver is repairable - just add new surrounds. While having the procedure done by a professional is not a bad idea, it's not terribly difficult to replacee speaker surrounds, and it's a great way to get a terrific deal on speakers - many really excellent old speakers are viewed as worthless simply because people do not know how to do this simple repair.