Engines are used to power all buildcraft machines such as mining well quarry, and refinery. There are three types of engines redstone, steam, and combustion engines. Redstone engines can be powered with redstone. Steam engines need to have coal inside and be powered with redstone. Combustion engines need to be powered with oil and cooled with water.
Redstone engines are used mostly to power wooden pipes. However they can be used to power machines very slowly. To power a quarry you will need 4 redstone engines.
Steam engines greatly improve the power that redstone engine produce they are used to power any machine. It takes a burnable resource to run, such as wood or coal.
Combustion engines are the highest engry producing engines, the downside is that you need to have fuel, oil, or lava to run them. Along with needed fuel they need water to cool them. If a combustion engines stops getting water and overheats it will explode.