Burst Damage is when you spam your hardest hitting abilities that usually also cost the most Action Points as quickly as possible. The point of burst damage is to spike your DPS as high as possible with little regard to longevity in the fight. When trying to deal burst damage you will attempt to do the most damage possible in the shortest amount of time possible, the quicker and harder the better.
Normally towards the end of a fight where your enemy has potential to escape or heal you'll want to apply as much burst damage as possible to prevent the heal from casting or enemy from escaping. Because the best burst damage abilities typically have a cooldown associated with them you may wish to keep them readied for the end of a fight.