Ever said to yourself "I don't have to worry about that. Something like that has never happened before," and then had that exact thing happen? That's what aggregate excess insurance is for.
Aggregate excess insurance provides financial protection against high losses...an amount of losses that precedent suggests will likely not happen. The policy sets an amount. Any losses above that amount are covered by the insurance company. Below that level, the customer is on their own. However, the coverage level is purposely set very high, higher than any losses are likely to reach.
Think of it like regular insurance with a really high deductible. The goal is to protect the customer against catastrophic events that are not likely to occur, but would ruin them if they happened.