From Diablo Wiki
Burst refers to, in the realm of gaming, damage output that isn't reliable. By that, it is meant that burst damage comes out in precisely that--a burst. There will be times when the damage output of a character is very high--exceeding the baseline--and other times when it is low, and is below the baseline.
This term has evolved from online RPGs and MMOs mostly due to the profluence of critical hits in gaming. In general terms, a critical hit will double the damage of an attack. So an attack that hits for 5 damage will end up dealing 10 damage. Many games also let the player augment the base damage of an attack, so that the damage from a critical becomes magnitudes larger. When one of these criticals actually hits, it is a very damaging attack, and is known as a burst of damage.
A "bursty" character, however, isn't limited solely to critical hits. In a game like Diablo II, a bursty character can also be one who has a large amount of the modifier, for instance. Bursty characters often rely on either a low-percentage attack that isn't guaranteed to hit, or a proc from an item or skill.
In some other rare cases, "burst" can also refer to the behavior of a monster or NPC. In Diablo III, for example, the Grotesque monster will burst upon death and release a large number of lampreys that will attack the player. Sometimes this type of monster is also known as a "burster" or "bursty".
- More reference terms.