"Ships" refers to a relationship between characters, generally a constructed one, although it can refer to a canon relationship.
If a fan or fic writer pairs one character with another, they are said to 'ship' them, eg. I ship Bobby and Dean.
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 between them like John/Bobby - hence the term Slash.
- The Pros and Cons of Shipping by TVGuide, October 2012