Lloyd's is an insurance market. It provides a framework in which buyers of insurance can be matched with sellers. It is not an insurance company;
Lloyd's is particularly popular for risks that are hard to place elsewhere.
As with any market it has its brokers, and there are many insurance brokers that bring business to Lloyd's.
On the other side are investors who underwrite risks through Lloyd's syndicates that are run by managing agents.
Each syndicate is, in essence, an insurance company. The syndicates pay claims, not Lloyd’s itself. This is why Lloyd's can be described as a market: its function is to match the syndicates with their clients.