It was developed by British Airways and Air France in the 1970s as the first supersonic passenger/civilian airplane.
Ultimately the cost of flying the aircraft was more than the revenue that it generated. The Concorde began a steady decline to retirement after the firey crash of Air France Flight 4590 which killed 113 people, and again suffered setback after September 11th, 2001. Even with the best safety record in airline history, the crash combined with the terrorist attacks led to passenger fear and low sales. Airlines that operated the Concorde eventually lost money on most flights, and long term operations were simply not sustainable. To make matters worse, it was very limited to which airports it could fly to in the US: JFK, IAD and DFW. The FAA was opposed to the Concorde for pollution, noise and fuel inefficiency concerns.
British Airways cites mostly political reasons for the ending of its Concorde program. They claim that the Concorde would have remained profitable had Airbus retained the airplane. However, there was also speculation that, due to the dwindling numbers of passengers, BA realized that it could make more money carrying passengers subsonically across the Atlantic.
Why did Air France retire the Concorde
It wasn't making money - in fact, it was losing money. Huge fuel price increases shortly after it was brought in meant it was never really profitable for Air France. Then double-whammy of the Air France Flight 4590, followed a few years later by 9/11 hitting Airlines hard in reduced passenger numbers (particularly into New York), caused Air France to consider it no longer viable to run even as a loss-making flagship service.
Why did British Airways retire the Concorde
A related but separate question, BA actually found a way to make their Concorde's profitable later on. They discovered that the public (particularly the business users who weren't paying for their own tickets...) thought Concorde tickets were more expensive than they actually were, so merely increased the price to match. They were profitable for several years until Airbus announced they were no longer going to maintain or support the aircraft.
The Concorde did fly for several years, but it couldn't fly supersonic over land (as Steve pointed out, it was able, but not allowed due to concerns about the sound of the sonic boom) and it guzzled fuel. In the end, it wasn't economically viable.