Burst of Speed is one of three buffing abilities at the Assassin's disposal, the other one being Fade. Burst of Speed raises the speed of the Assassin, making her both faster in her attacks and movement. Burst of Speed attack speed increases are transformed differently into EAIS (used in calculations to determine the frames per attack) than regular ias is; what this means, is that Burst of Speed has the capacity to increase the assassin's attack speed much more than other ias sources (as from gear).
Most builds will only need 1 point to Burst of Speed, however a few builds may require more points to hit max frames (fastest attack speed) depending on the weapons and gear. It does have diminishing returns.
It is also important to note that some builds may not use Burst of Speed at all if Fade is needed for damage reduce or resist purposes. Fade and burst of speed cannot be used simultanously.