Equipment is essential in RPG's. What would a shiny world-saving hero be like with a rusty dagger that he found when he was still a kid, and this cooking pot that serves him as a helmet.
It also helps to keep the player entertained along the game. Don't you want to exchange this rusty dagger with a saber that is sold in the shop for 100 pieces of gold, maybe a real helmet aswell, so you can finally beat those monster in the woods with ease?
Equipment can be devided into the following categories:
Weapons - Daggers, swords, staffs, rods, clubs, bow and arrows, guns anything you want really.
Armor - From gauntlets to full body armor or a magic tunic.
Accessories - A statboosting, armor increasing, kick-ass Ring of Aralarythrilim and the likes.
Any Equipment can also have effects. A short and light dagger for example might deal 2 times damage, or special bow is made to fire 3 arrows at once. A magical headband can increase a magic attribute along with armor and well made boots can give a speed bonus.
Some games also feature special items (like Final Fantasy 7's materia, that can be equipped to weapons and armor for magical application) so think of anything you can put on you or your weapons and give it an effect that would fit to its purpose.