Mana is used to cast druid, mage, paladin, shaman and warlock spells. It is similar to energy, focus and rage in that it is consumed to trigger certain abilities. A blue mana bar underneath a player's health bar indicates how much mana a caster has at their disposal. The bar starts at full and is depleted over time as spells are cast; unlike energy which is a fixed amount or rage which requires specific actions to fill up from zero.
Mana recharges at a rate that's dependent on a character's level, spirit and intellect; see Mana regeneration for more info. Some talents and buffs also increase the rate at which mana replenishes over time.
Mana regeneration (mana regen) during combat is slower than while out of combat. Mana is gained immediately during combat by drinking potions made through Alchemy or while not in combat by consuming drinks.
If a caster runs out of mana they will no longer be able to cast most spells. This is called going 'out of mana' or 'low on mana' and the command for this emote is /oom. Ways to increase a character's mana include: obtaining special gear with intellect or spirit bonuses, choosing mana regen talents, buffs or potions and considering how much damage a spell does in relation to mana it costs; referred to as 'damage per mana'.
Base mana refers to how much mana a character has before being modified by intellect, spirit and effects from items. Multiple spells require a percentage of your base mana to be cast.