A four-cylinder engine is an internal combustion engine that has four cylinders. The cylinders are aligned in a straight line and they fire in order. The first cylinder to fire is the one closest to the flywheel (the large wheel at the back of the engine). The next cylinder to fire is the one on the other side of the flywheel, and so on.
The pistons in a four-cylinder engine go up and down in their cylinders. When they're all the way at the top, they make what's called a compression stroke. This is when air and fuel are compressed into a small space before being ignited by a spark plug. When this mixture ignites, it expands rapidly and pushes down on the piston. This downward force turns the crankshaft (the long shaft that runs along the bottom of the engine), which ultimately powers your car's wheels.
Four-cylinder engines tend to be more fuel efficient than larger engines because there's less weight to move around (fewer pistons = less mass). They also tend to have fewer emissions because they burn cleaner than larger engines.