A two-handed weapon is a weapon whose weapon size is one category larger than its wielder. (That is, a large weapon for most player characters, and a medium weapon for gnomes and halflings.) These weapons require two hands to wield, so while they only occupy the main hand slot, they also block equipping anything in the off-hand slot. The most significant consequence of this may be the inability to use a shield while wielding a two-handed weapon.
The advantage of using a two-handed weapon is having the strength modifier (if positive) increased 50% (rounded down) before being added to damage inflicted by the weapon.
Weapons more than one size category larger than the wielder are not considered two-handed weapons because they cannot be wielded at all.