A rapier is a type of sword which emerged around the 16th century, completely changing the face of swordplay. Early versions of the rapier were produced as early as the late 1400s, but the sword really came into its own during the Renaissance, becoming a must-have accessory for gentlemen in all walks of life. Several schools of rapier fighting emerged during this period, and some modern schools of rapier fencing are descended from these earlier dueling clubs and training facilities.
The exact definition of a rapier is actually a bit flexible, which can be confusing. As a general rule, a rapier is a slender, lightweight sword designed for single-handed thrusting use, and it typically has a complex guard and handle which is designed to protect the hand of the wearer. Rapier blades and handles took a variety of forms, however, as you can see if you visit a museum with an ample display of Renaissance weapons.
The advent of the rapier was quite revolutionary for its time, because the blade was designed for thrusting, rather than cutting. This design shift also changed the way that people approached the use of the sword, with people developing lightning-quick thrusting fighting styles which were quite aggressive, and designed to put people off-guard. Many people carried rapiers for the purpose of self defense, especially in urban areas, and the blades became popular for dueling.
A rapier which has been designed for practical use has a stiff blade, ensuring that the blade will penetrate the body of an opponent. Historically, people often noted that rapiers had a tendency to break, especially in the hands of people who were not experienced, and as a result rapiers were reinforced with heavy central sections and people were taught a variety of techniques to use them effectively. Rapiers could be used against other styles of swords, both as defensive and offensive weapons, and in the right hands they could be effective against armor.
The modern rapier is somewhat difficult from the historical version. People who fence with rapiers generally do so for sport and pleasure, rather than out of a desire to kill their opponents. Therefore, the blade has been modified to make it less lethal. Modern rapiers are extremely flexible, so that they bend when they come into contact with the human body, rather than penetrating. Like rapiers of old, a quality rapier is well balanced and it feels lightweight and strong in the hand, facilitating an agile, extremely active style of fencing which can be beautiful to watch.