Rate of fire is how many attempts at damage a bombard unit gets per shot. For example:
When you fire a catapult (rate of fire of 1), the computer "rolls the dice" once. If you hit, you do 1 point of damage. If you miss, no damage.
When you fire an artillery piece (ROF of 2 I think), the computer "rolls the dice" twice. Each time you have a chance of doing damage. So an artillery piece can do 0, 1, or 2 points of damage each time it is fired.