A booster rocket was a rocket used to provide added boost when a spacecraft was launched from a planet's surface.
Late-20th and early-21st century space shuttles used booster rockets to help them reach orbit. According to Shaun Christopher, every astronaut was relieved when the booster rockets, which he compared to Roman candles, fell off of the space shuttle. (TOS novel: The Rings of Time)
Booster rockets were also equipped on levitation boots in the late 23rd century. James T. Kirk instructed Spock to use the booster rockets in order to escape from Hikaru Sulu and members of the Galactic Army of Light in Turbo shaft 3. (ST movie, novelization & comic adaptation: The Final Frontier)