Wands are one-handed weapons used by spell-casters in Diablo III. These are not class-specific items, but it seems that only Wizards and Witch Doctors can equip them. Barbarians, Monks, and the Fifth Character are not permitted to equip or use wands.
As in Diablo II, the magical modifiers found on wands will primarily benefit spell-casters. Expect bonuses such as faster casting speed, +%magical damage, and +%experience gained.