Insurance companies pay out claims. A cynic might argue that insurance companies are in the business of not paying claims, and point to the pages and pages of fine print in any insurance contract as proof.
Maybe. It's probably true that insurance companies are more in the business of collecting premiums than they are in the business of paying off claims. But eventually, any insurance company will have to pay out some money at some point, despite the best efforts of actuaries and lawyers. Thus, the claims reserve.
The claims reserve represents money the insurance company has set aside to pay for claims. The claims haven't been settled yet...think of it like a special pile of cash sitting around waiting to get paid out.