Speed affects the speed at which a character moves while running. Speed is a movement attribute, and can be useful in a number of situations, such as when fleeing from or pursuing foes, or when attempting to avoid area of effect attacks.
All classes can benefit from increased Speed, however, melee classes like Assassins, Gladiators, Templars, and Chanters may find more benefit than others as increased Speed will allow them to close the gap between their foes faster.
A high Speed attribute allows players to reach their destinations faster, and thus, Speed is an important attribute for all classes. However, the only means by which players can increase their Speed is with feet slot armor, buffs, scrolls, and titles.