a member of Lloyd's, the international group of insurance underwriters based in London. The Names are wealthy people who accept a financial risk in an insurance contract, and in return for this they usually make large profits. Sometimes, however, they lose a lot of money when events happen which affect insurance companies, such as serious accidents involving ships or planes, or severe weather conditions that cause a lot of damage.
Definition from the Longman Dictionary of Contemporary English Advanced Learner's Dictionary.