"C/o" stands for "care of." It is an abbreviation used to send correspondence to a specific person when he is not likely to be there. This is especially useful for sending things to a work address or to people who can only be contacted by a third party.
The way to use "c/o" is to put the intended recipient's name on the top line, then begin the second line with "c/o" followed by the actual recipient's name. This can also be a way to invite a mutual friend when you don't know his address. This is accomplished by listing the friend whose address you do know as the actual recipient and the mutual friend as the intended recipient.