Old guy, head of the catholic church, elected by cardinals of the catholic church. Normally offically celibate, although some noteable exceptions occur to this during the medeival period.
During the medeival period, could have enormous power (see crusades). Theoretically there is only one pope, however several times during the middle medieval ages there were several popes simultaneously, with the other popes (whichever one wasn't on your side) called the antipope.
The modern pope lives in Vatican, a religeous city state in Italy, but originally the pope lived in Rome (I beleive), although a few popes and antipopes set up their capital elsewhere. At some stage (probably during the medeival period) the pope settled in the Vatican for good.