Answer:
Fencing is a sport of three different types, or styles of fighting: Saber, Epee, and Foil. These three different styles have different target areas, rules, and ways of getting a touch (a point).
Saber:
Target Area: The torso, mask, and arms.
Way of Scoring: You can get a touch by slashing your weapon on your opponent.
Weapon: A saber sword is usually the sword you see in movies or plays. It has a bellguard, which curves around to connect to the grip.
Epee:
Target Area: The whole body, and yes, including the shoes.
Way of Scoring: You can get a touch by stabbing your opponent.
Weapon: An epee sword is noticeably heavier than any other sword. It is basically a saber sword, with a larger bellguard and, of course, heavier.
Foil:
Target Area: The torso, excluding the arms and mask.
Way of Scoring: You can get a touch by stabbing your opponent.
Weapon: A foil blade is just a bell guard and grip. If you can imagine a sword (with a fencing blade), and a bell guard instead of the hilt, this is a close image of a foil sword. The grip can either be a pistol grip or french grip. This is the weapon I favor, and my personal favorite weapon is a Belgian-grip Foil.