Aside from fights being broken up into phases, some bosses have enrages or frenzies. Changes have been made to the terminology here for clarity in boss fights.
Basically put, when a boss enrages (eg. Magmadar in Molten Core), the enraged state can be dispelled with Tranquilizing Shot; when a boss frenzies (eg. Maexxna at 30% health), they do more damage and this should be dealt with (by extra healing, warrior tank popping Last Stand, etc); when a boss berserks (eg. Netherspite), you have taken too long to complete the fight, which has been designed with a time limit in mind. Source: Daelo.
Gaiwyn of Proudmoore