Not to be confused with Deep Space Maneuvers
All space missions have trajectory correction maneuvers, also known as TCMs. Their purpose is to adjust the trajectory.
Trajectory correction maneuvers are conducted after or before a rocket reaches an important milestone of its mission (for example after setting a trajectory towards another planet or before reaching its sphere of influence).
Also, trajectory correction maneuvers are almost always done by burning the engine sideways from the flight path. They usually don't accelerate or decelerate the rocket, but slightly change its trajectory.
Trajectory correction maneuvers are important for precision adjusting the path of a rocket. For example, while orbiting the Earth, a rocket is affected by the gravity of the Moon. One might want to set the trajectory in such a way that it will intersect the atmosphere of Mars for an aerobraking maneuver, but from Earth's sphere of influence this is risky. However, once the rocket is in a heliocentric orbit that is between Earth and Mars, this becomes possible.
Sometimes, deep space maneuvers are not enough to send a rocket to the desired path for a flyby. In that case, additional trajectory corrections are needed.
One of the most impressive way to do trajectory corrections is when a rocket is just entering the sphere of influence. By burning the engine sideways, it is possible to change the trajectory from a prograde to a retrograde one. This can have tremendous effects for gravity assists.