Rate of fire is the number of chances a bombarding unit has of damaging its target, or the maximum number of hitpoint damage it can inflict per attack.
For example, a cannon (RoF:1) can possible knock a rifleman from 4 HP down to 3 HP, but an artillery piece (RoF:2) can damage the same rifleman from 4 HP to 2 HP in a single attack.
Every time you bombard you attack the enemy a number of time equal to your rate of fire. If each bombard is successful, you take hit points equal in number to the attacking units rate of fire. If some of them aren't successful, you take less hit points, and if none are successful (guess!).
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