A case of rapier is a matched-pair of fencing weapons (levels of "matched-ness" depend on the person). The name comes from the fact that they used to make the pair of rapier in a way that they would both fit into the one scabbard - a case. This is also known in the SCA as fencing Florentine, and some people call it "fighting two-swords."
The basics of this style involve using one weapon offensively, trying to strike one's opponent, the other defensively, trying to confuse, parry, and misdirect the opponent. The joy of the style is in switching which weapon, exactly, is being used for what. The downside is that it's very hard to effectively use both hands simultaneously, and that in melees you tend to get "picked on," although a good Florentine fencer can hold two moderately good single-weapon fencers to a standstill.