The ingame tooltip reads: "Affects a ship's combat order and increases chance for successive strikes."
During battle, the commander with the highest speed will move first every round, then the commander with the second highest speed will go second, and so on. This is very advantageous as you can debuff, reduce stacks of, or even destroy entire fleets before they can attack you. A "successive strike", also known as "double attack", is an alternate version of a critical hit.
One important thing to note is that when two fleets occupy the same space, and a fleet attacks with the "closest target" setting, the fleet will always target the fastest fleet on that space. Therefore, any ballistic fleets should have less speed than your tank fleet.