When a company buys insurance, the policy usually comes with a coverage limit. This provision caps the amount of damage covered under the policy.
So if a little bad stuff happens (a small fire in the back of the factory), the insurance company will pay the damages. However, if a lot of bad stuff happens (a rampaging herd of elephants flattens the entire corporate campus), the coat might be more than the insurance company agreed to pay.
What's more, if the aggregate limit is breached (meaning the total amount of damages covered for a given time period) the company could be exposed every time something else happens. (What if the elephants come back? What if they bring their giraffe friends?)
Thus the aggregate limits reinstatement. This clause resets the total loss limit for an extended period of time. The company will likely have to pay in order to invoke this clause, but it's better than being effectively uninsured.