"Ships" refers to a relationship between characters, either one constructed by fandom or a canon relationship. It's usage has been traced back to The X-Files fandom in the early 1990s.
If a fan or fic writer pairs one character with another, they are said to 'ship' them, eg. I ship Jody and Donna.
Ships are usually granted a mashup name, which is a portmanteau of the characters involved eg Destiel for Dean and Castiel. The pairing may also be written with a slash (or "virgule") between them like John/Bobby - hence the term Slash.