Lloyd’s (http://www.lloyds.com/) is an insurance market, and is not a provider of insurance in itself. It is the insurance equivalent of the stock market, except instead of stocks being traded, risks are traded. A risk would be e.g. insuring a ship, the risk a ship will sink. Risks are split between insurers as no insurer will want to expose themselves 100% of any big risk.
Lloyd’s is not a retail market; you cannot insure anything there unless you have a seriously large contract. The general public is obviously not allowed inside.
When a customer has a risk, they will employ an insurance broker, who will go to Lloyd’s, and also around other companies, who are not members of Lloyds, and try and seek the best deal on each ‘slice’ of the risk. Insurers in the Lloyds market are called syndicates. They used to be numbered (e.g. Syndicate 780 (Advent Insurance)), but now only the oldest syndicates still use numbers.
Each syndicate has what is effectively a stall on the market floor, and brokers literally walk around the market and bargain with underwriters to get the best deal on any risk.
Lloyds is based in the Lloyds of London building