A booster is a rocket used either in the first stage of a multistage launch vehicle or in parallel with longer-burning sustainer rockets to augment the space vehicle's takeoff thrust and payload capability. Boosters are traditionally necessary to launch spacecraft into low Earth orbit, and are especially important for a space vehicle to go beyond Earth orbit. The booster is dropped to fall back to Earth once its fuel is expended, a point known as booster engine cut-off (BECO).
A GEM-40 strap-on booster for a Delta II launch vehicle.
A multistage rocket or step rocket is a launch vehicle that uses two or more rocket stages, each of which contains its own engines and propellant. A tandem or serial stage is mounted on top of another stage; a parallel stage is attached alongside another stage. The result is effectively two or more rockets stacked on top of or attached next to each other. Two-stage rockets are quite common, but rockets with as many as five separate stages have been successfully launched.
Each stage of the Black Brant 12 sounding rocket has its own set of tail fins.
The second stage of a Minuteman III rocket
Cutaway drawings showing three multi-stage rockets
Apollo 11 Saturn V first-stage separation