I think the College of Cardinals has been around in one form or another since the Middle Ages. They once held a huge amount of power over the affairs of the Roman Catholic Church but as the process of choosing a pope became more refined, their influence has steadily declined.
Who are they?
Actually the College of Cardinals is broken down into three different orders. They are:
Cardinal Bishops – these guys (sorry ladies, the Roman Catholic Church is still a little behind the times when it comes to the subject of women) are the bishops of the suburban areas of Rome. These include the ‘burbs known as Ostia Palestrina, Porto and Santa Ruffino, Albano, Velletri-Segni, Frascati, Sabina-Poggio and Mireteto. This select group is specifically appointed by the Pope. The dean of the College of Cardinals also is elected from members of this group and is given the title See of Ostia along with his regular duties as bishop in one of the aforementioned suburban areas.
Cardinal Priests – I guess these guys are next in the pecking order. Their members include cardinals who are bishops but the diocese that they are responsible for lies outside of Rome.
Last but not least, you have your Cardinal Deacons. These esteemed members hold the title of bishop but are assigned to full time service in the Roman Curia. That is to say, they are not assigned to a diocese and spend their time in Rome advising the Pope. Not to worry though, after ten years of faithful service in that role, they can request a transfer to the order of Cardinal Priests. The oldest member of this group also has the honor of announcing a newly elected Pope to the general public.
What do they do?
Sure, the Pope is supposed to be infallible but a little advice now and then couldn’t hurt could it? One of the main responsibilities of the College of Cardinals is to keep the pope up to date on worldly matters and offer up their advice accordingly.
Their real claim to fame though is that they are responsible for choosing a new pope amongst themselves when events warrant such an occasion. If you're interested and would like more information about how they accomplish this, please see the w/u How a Pope is chosen.