The three primary weapon types are foil, epee, and sabre (or saber).
A foil is long, narrow, and flexible mostly in the vertical direction, if you are holding it. Practice foils will have a rubber tip on the end, but competition (electric) foils will not – they will have a small spring-loaded metal tip that determines if you hit someone hard enough to score a touch. These tips are not sharp, and will not break the flesh. Foils are intended for stabbing, not slashing.
An epee is similar to a foil, but it is less flexible. It is also a stabbing weapon.
The sabre is a slashing weapon and can be easily identified by their larger bell guard that protects the fencer’s hand. Sabres are very flexible and can be whipped around quite easily.
Citation for the picture: http://postfiles11.naver.net/20101122_298/petiteguy_12903921018957bpe8_JPEG/fencing-weapons_1.jpg?type=w2