Underwriters are companies carrying the risk of an insurance policy, so in the event you make a claim, the underwriters are the ones who would pay out if and when your claim is approved. Sometimes it's the same company as the one selling the insurance policy and sometimes it's a different company.
In our case, the underwriter for our buildings and contents covers is Casualty & General Insurance Company (Europe) Limited (CGICE). The underwriter of our Home Emergency and Legal Expenses policy (if you have it) is ARAG Legal Expenses Insurance Company Limited.
To see the definitions for other commonly used insurance terms, check out our dictionary.