From back of packet: "Clean, safe and easy to use, Blu-Tack provides an easy alternative to drawing pins and sticky tapes with hundreds of uses around the home, office or school environment." The brand name is actually Blu-Tack.
Old blu-tack can be revived by rolling it between your hands for a while. Maybe something to do with heat or oil from your hands... I have no idea how it's sticky. It's just cool like that.
Can be used to hold bigger things up - but beware of trying to stick smooth things or smooth surfaces. It doesn't work very well (I stuck a pair of lightweight active speakers in a corner above my bed with blu-tack... thought it was nifty until they fell down...luckily my bed was there to stop them smacking against the floor...)
To remove little bits of blu-tack left over when you remove a big wad from the wall, get a nice big blob of the stuff and rub or roll it over the left-over fragments, which will then be assimilated into the blob. It can also (according to the packet) be removed with lighter fuel or dry cleaning fluid. Just don't smoke while you're doing it, I guess...