A lime is a fan fiction story that stops short of full, explicit descriptions of sexual activity. A common analogy is that it is PG-13 action, as opposed the NC-17 kind of fanfiction or lemons, where limes are not quite as explicit as the lemon. Another definition is that it includes everything up to, but not including penetration, but that can be a subjective call.
Other forms of limes are those stories that approach an intimate scene, and then go "off-camera", with the intimacy left to the reader's imagination. As with the other terms of this type, the orientation of the characters involved (such as the slash yaoi and yuri pairings) are not as important as the kind of intimate activity engaged in.