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Objects caught in the sun's orbit will loop around in large elipses, while objects just passing by will do so in a parabola trajectory.

This is because of the sun's gravity. Since the sun is a sphere, it pulls on everything in every direction. There is no spot where it is not pulling.

When an object gets tracked into the gravitational pull, it doesn't loose its initial velocity, so it keeps going forward, but now it is also being pulled toward the sun. Some objects become trapped in orbit around the sun, continuously falling around it in that elliptical pattern. However, some objects don't get pulled into orbit. The sun simply alters their path a bit.