With each level of this perk, you get +2 AP each turn that can only be used for movement.
The counter only shows up to 10 Action Points but internally it keeps track of any extras. The extras AP of Bonus Move is invisible in Fallout, but yellow in Fallout 2.
In both, Fallout and Fallout 2, this perk can be exploited by reloading a save that is in combat, the extra movement AP will be available for use again, allowing further movement in a single round. On the other side of the coin, in Fallout, running out of "normal" AP ends the turn whether or not there are extra movement AP left.
In Fallout Tactics with each level of this perk, you get to move 20% further per AP.