Burst damage is a term used to describe dealing high amounts of damage in a very short period of time. Spells which qualify for burst damage are often Mana inefficient.
Doing burst damage normally causes the player to be out of mana much faster. In some encounters, burst damage is necessary. Its main purpose in PvP is to bring an enemy down fast, often combined with Focus Fire, giving enemy healers as little chance as possible to heal the damage inflicted.
Certain classes are better at burst than others, and certain specs of these classes.