In astrodynamics or celestial mechanics a parabolic trajectory is a Kepler orbit with the eccentricity equal to 1. When moving away from the source it is called an escape orbit, otherwise a capture orbit. It is also sometimes referred to as a C3 = 0 orbit.
Under standard assumptions a body traveling along an escape orbit will coast along a parabolic shaped trajectory to infinity, with velocity relative to the central body tending to zero, and therefore will never return. Parabolic trajectory are minimum-energy escape trajectories, separating positive-energy hyperbolic trajectories from negative-energy elliptic orbits.
Read more about Parabolic Trajectory: Velocity, Equation of Motion, Energy, Barker's Equation, Radial Parabolic Trajectory