The rapier was a sword used originaly in the 16th and 17th centuries, primarily as a civil weapon (meaning, not used in war). Its use was most common in duels. Later, towards the 18th century, the weapon, along with the tatics used, changed. Modern fencing is based upon the 18th Century weapon and tatics.
The Renaissance style rapier is made up of the following parts:
The Blade - A sharp tip, and two edges. It is divided into 3 sections. The forte, foible, and tang. The forte is the lower, stronger part of the sword, and is used in parrying. The foible in the upper weaker part of the blade, commonly used for cuts. The tang is the section of the blade that goes through the handle.
The Guard - The guard came in many forms, buts main pupose was to protect the hand of its user.
Quillons and Knuckles - On some weapons knuckle guards are attached. They are used to product the hand, primarily the knuckle. The Quillons are used for parrying and catching the oppenents blade.
The Handle - The part of the blade you hold. Typically made out of a hardwood.
Pommel - Screws onto the bottom of the handle, and holds the sword together.
Note: The Websters dictionary points our the rapier was only used for thrusting, this is by far not the case. The weapon only does its most damage when thrust, however countless duels have been won when never a thrust struck.