A double-sided weapon is a weapon designed such that both ends can be used to strike opponents. Even though these are large weapons and require two hands to wield, they do not get 150% of the strength modifier added to the damage inflicted; instead, hits from the main end have the normal (full) strength modifier added to damage, while hits from the off-hand end get half that amount added to the damage.
Wielding a double-sided weapon automatically causes one to be dual-wielding, allowing an extra attack (or two) per combat round and incurring the standard dual-wielding penalties. These penalties are not as severe as possible, as a double-sided weapon's off-hand end counts as a light weapon, and they can be further ameliorated (as usual) with the dual wielding feats (ambidexterity and two-weapon fighting).
One advantage of using a double-sided weapon instead of two weapons is that both ends inflict base damage comparable to medium-sized (non-light) weapons, yet the attack penalties are those of using a small (light) weapon in the off-hand. Another advantage is that a single spell (such as magic weapon) can enchant both ends of a double-sided weapon, whereas it takes two spells to enchant two weapons. Yet another advantage is that being a single weapon, one only needs to use one feat for weapon focus and/or weapon specialization instead of two, unless using a light weapon in the main hand or suffering the penalties of using a non-light weapon in the off-hand. The major disadvantage of double-sided weapons is that they are exotic, and thus require a feat investment to wield. They also necessitate a weapon switch if a shield becomes desired in some circumstances, which could affect the applicability of weapon-specific feats (such as weapon focus).
The double-sided weapons in Neverwinter Nights are the dire mace, double axe, and two-bladed sword.