Finally! A topic that I actually know something about. I've been a member of the forum since God-knows-when, but haven't had anything useful to contribute. Anyway, at the risk of going over things that everyone knows, a co-op is a building that's owned by a corporation in which the residents own shares. Unlike a condo, where you actually own real estate, co-op members only own stock that grants them the right to reside in a particular unit.
Not all co-ops are older buildings, although they tend to be. There are several reasons that an apartment building may want to convert to a co-op instead of a condo. On one end of the spectrum, sales prices tend to be lower so low-income residents of an apt. building may have an easier time buying in when the building converts. At the higher income end, a co-op board has the right to approve members (unlike a condo), so they can keep the building "exclusive." IMHO, there are more negatives to co-ops than positive. First, they're difficult to finance -- many banks won't lend to co-op members. Second, they're a bit harder to sell -- there are only a few title companies around that are experienced in co-op transfers. Third, boards have a lot more power than in a condo to regulate your use of the unit(some people find that to be a positive, though).
That's just my opinion. Other people really like co-ops, so I guess it depends on what you're looking for.
