In computing terms, it means to install or connect something. It can also mean starting a relationship with another person. Actually, the way it's often used in modern slang, it refers to a casual sexual experience of some kind. Depending on who's talking (a college student is probably going to expect more out of a hookup than a sixth grader), it can mean anything from making out to intercourse. Some young people use the term "hooking up" to refer to hot-and-heavy action in the context of a committed relationship, but general references to hooking up or to the "hookup culture" imply casual experiences with no romantic relationship implied or intended.
It can also mean "to give," as in: "Hook me up with some shoes."
See wiktionary:hook up for more uses.