Cooldown is the number of seconds it takes to wind back for another attack after the attacking animation has played. With Ranged weapons this is the amount of seconds required before the weapon can be fired again. Higher Fitness and Strength levels will reduce the cooldown time for melee weapons.
Typically Heavier weapons have higher cooldown values, tiring out your survivors in a few swings, while lighter weapons are easier to swing but deal less damage.
More information can be found on the Weapons page.