The Frame Delay is a hidden unit attribute in the Age of Empires series. It determines the number of frames (which measure time) a unit needs before attacking a newly selected target. So, as with the Rate of Fire, the lower that value is, the faster the unit starts the first attack.
As opposed to the Rate of Fire, the Frame Delay only applies that one time when a target is attacked the very first time. As long as that target is attacked, the Rate of Fire applies from the second shot on.
Most melee units have a Frame Delay of 0, which means they instantly turn to new targets and attack. Ranged units, however (most notably Cavalry Archers), often have a frame delay. That weakens hit-and-run tactics and helps melee units to stand a chance against ranged opponents.
The Frame Delay is not shown and cannot be upgraded or influenced in any way within a game.