So, all air-breathing heat engines (from internal combustion engines in your car to supersonic aircraft engines) require the air to be compressed above atmospheric conditions before you add fuel and combust it. The more you can compress the air before igniting it, the easier it is to extract the energy from the reaction and use it for work or thrust.

For engines designed for really really high speeds this gets tricky as the physics behind how air flows get really wonky when you get up to the speed of sound or faster, which can make it really really difficult to compress the air (and, more importantly, make it really difficult to make a single kind of engine that can compress both subsonic and supersonic airflows).

Turbojets are just turbine engines, where the airflow is run through a series of compressor blades on the inlet of the engine. These are outwardly similar to the engines on most jet aircraft, although modern engines are turbofans, which bypass a significant portion of the air around the compressor for efficiency reasons (instead of in a turbojet where everything goes into the compressor).

Ramjets have no compressor blades, and instead are ducted in a special way to use the aircraft's forward momentum to compress the air as it enters the engine ducts. Scramjets are the same concept, but are used for even higher speed airflows (ramjets compress air to subsonic velocities inside the engine before combustion, scramjets allow it to remain supersonic). However, this poses a problem at low speeds, because without the forward motion of the aircraft, the ramjets don't work.