The term horsepower was invented by the engineer James Watt. Watt lived from 1736 to 1819 and is most famous for his work on improving the performance of steam engines.
In Watt's judgement, one horse can do 33,000 foot-pounds of work every minute. So, imagine a horse raising coal out of a coal mine. A horse exerting 1 horsepower can raise 330 pounds of coal 100 feet in a minute, or 33 pounds of coal 1,000 feet in one minute, or 1,000 pounds 33 feet in one minute. You can make up whatever combination of feet and pounds you like. As long as the product is 33,000 foot-pounds in one minute, you have a horsepower.
If you want to know the horsepower of an engine, you hook the engine up to a dynamometer. A dynamometer places a load on the engine and measures the amount of power that the engine can produce against the load.
The term horsepower today is used by every manufacturer to give consumers a definitive idea of just how powerful a car is. While horsepower was originally used, it also has a lot of derivatives like brake horsepower (bhp), kilowatt (kW), PS, and a lot more. Depending on the region you're in, a unit of horsepower is used, but they are all determined using the same intrinsic values.