Mana is the magical energy used by characters in the Diablo games to cast spells or use skills.
Background
Mana is what the primal arcane magical force that pervades Sanctuary is usually called. Individuals skilled in sensing this power can channel the spiritual essence stored in their bodies through different techniques in order to accomplish great feats that they would be physically incapable of doing.
Mana Attribute
In Diablo 3, Mana will not be used by all classes. The Barbarian, for instance, uses Fury instead to make more sense with the world lore and gameplay mechanics. No specific Attribute is increasing the Mana pool of a character, but Vitality is increasing Mana regeneration. Mana regenerates very slowly and characters who use mana will have to rely on Mana Globes and any skills that may be at their disposal to increase their reserves.