Why is diesel is an internal combustion engine?

When air is compressed it becomes hot. A diesel engine compresses air and fuel in a cylinder. The mixture burns and pushes down the piston. It is called an internal combustion engine because engines that work by burning fuel inside a cylinder and pushing down a piston are called internal combustion engines.

Steam engines are external combustion engines. The fire burns and heats water in a boiler. The water turns to steam and either drives pistons like in a steam locomotive or in a turbine.

Gas turbines could technically be called internal combustion but are not. One turbine compresses the gas. The gas burns under pressure in a combustion chamber and turns another turbine. Jet planes and a number of electric generators use gas turbines.