A rapier is a sword which has two edges on its narrow blade. In the time of Shakespeare, a rapier was a common weapon — it's even used by some of his characters.
A rapier is a particular kind of sword, used mostly for thrusting. Rapiers were especially popular in 16th and 17th century Europe. The long, slender blade of the rapier is lightweight and very sharp, and it usually has an intricate hilt, or handle, to protect the hand of the person wielding it. Because of its blade's characteristic sharpness, rapier is also used as an adjective: if you have a rapier wit, you are quick with the jokes.