A booster in space-related applications is usually a solid rocket booster: a solid fuelrocket of which two or more are attached to the main rocket to provide the main thrust in the initial phase of the rocket's flight. They form the first stage, though the second stage also starts operating at the beginning. After the first stage is discarded, the second continues. There are also liquid fuel boosters (see also Ariane 4), these are called liquid boosters.
Spacecraft aren't the only vehicles to utilise rocket boosters. Missiles (being atmosphere-bound rockets) often do also. For example, see 2K11 (SA-4) or S-200 (SA-5).
Rockets are used to accelerate, change orbits, de-orbit for landing Landing is the last part of a flight, where a flying animal or aircraft returns to the ground.
Modern rockets were born when, after receiving a grant in 1917 from the Smithsonian Institution, Robert Goddard attached a de Laval nozzle to a rocket engine's combustion chamber, doubling the thrust and enormously raising the efficiency, giving birth to the real possibility of practical space travel.
After the war, rockets were used to study high-altitude conditions, by radio telemetry of temperature and pressure of the atmosphere, detection of cosmic rays, and further research.