In celestial mechanics, around a body of great mass (such as a star), a parabolic trajectory is the 'border case' between a elliptical trajectory (which would lead to a closed loop, an elliptical orbit) and a hyperbolic trajectory (in which an object contains more than enough kinetic energy to escape). Therefore, it's the energy-cheapest trajectory that would allow the object to escape the gravity field of said object.
But that's just classical physics. It wouldn't necessarily apply to warp capable vehicles. (And there's no mass around which they fly, IIRC. Still, I suspect that's where it comes from.)