Having a weapon in hand--any weapon--will greatly increase a character's base damage by a certain amount. In addition, many skills require a weapon, or a weapon of a certain kind. While a character can attack bare-handed, there is no advantage to doing so, and even the poorest of weapons is a substantial improvement over an empty fist.
Weapons may be divided into two broad categories: melee and ranged. Some skills may only be used in conjunction with one of these two types of weapons. Melee weapons tend to scale with the user's strength; ranged weapons may scale with dexterity or with intellect.
Weapons may require one or two hands to use. Though some off-hand items (mostly parrying daggers) inflict additional weapon damage, there is no support for proper dual-wielding. Two-handed weapons also tend to be slower then one handed weapons.