It comes from the word relationship. It means who you would like in fiction to be in a relationship. So in Voyager fandom you have the J/C shippers who were rooting for Janeway and Chakotay to end up togther and the J/7 shippers who were rooting for Janeway and 7 to end up together. People refer to themselves as shippers sometimes to indicate that is a big part of their fandom interests.
Even though I have two shipping preferences (J/7 and K/S) I don't call myself a shipper because I'm not really into relationships in fiction much, or romance.