Glossary
A gear is a part of the gearbox, which in turn is part of the drivetrain, which is mounted on the engine and converts revolutions into torque, which in turn drives the wheels. The gearbox's task is to ensure efficient driving. Changing gears keeps the revs down, avoids overloading the engine and keeps fuel consumption down.
When you change gears, the interaction between the different gears in the gearbox changes. It generates different gear ratios. To suit different driving situations, the gearbox controls the engine's torque. The gearbox transfers the torque to the drive shafts, which drive the wheels.
On an automatic car, this happens automatically, while with a manual gearbox, you use the clutch as a bridge between the engine and the gearbox. You then press the clutch pedal to shift up or down.