A two-handed weapon (or abbreviated as 2H-sword/mace/axe) is a weapon that requires both the main hand and off-hand slots in use (as opposed to one-handed using one slot). Two-handed weaponry includes swords, maces, axes, staves, and polearms. Generally two-handed weapons are slower than their one-handed counterparts, but make up for it with stronger stats.
If the character equips a two-handed weapon, any item in the off-hand slot will un-equip. The off-hand is not usable when a two-handed weapon is equipped, even though the slot will appear empty. You can equip a two-handed weapon and a ranged weapon at the same time, as they use different slots. Warriors are the exception, however; due to Patch 3.0.2 they can dual wield two-handed swords, maces, and axes (spears and staffs are excluded) if they obtain Titans Grip, the Fury talent. Rogues can not use 2h weapons or any kind. mages, priests and warlocks can use 2 hand weapons in the form of staves.
Eligible classes no longer need to see a weapon trainer to learn this skill.