Is a comet necessarily confined to the solar system? I had the following question:


  A comet enters the solar system. Assume that it is influenced only by the Sun, not by any of the planets. Which statement about its orbit is correct? 


And I chose as correct statement:


  Its orbit might be an ellipse, or is might be a parabola or a hyperbola (because a comet is not necessarily confined to the solar system forever).


I want to know what it means by a comet is not necessarily confined to the solar system forever.

Does it mean that eventually the comet will "die" out, with the sun vaporizing all of its ice, so it will basically cease to exist while it is in the solar system?

Or does it mean that the comet can leave the solar system? If the comet enters the solar system it is subject to the mighty force of the suns gravity, then how can it escape?
It means that the sum of the kinetic and gravitational potential energies can be greater than zero. Such objects are not bound to the solar system. They fall towards the Sun on hyperbolic trajectories, picking up speed and kinetic energy as they do so. After rounding the Sun they then have enough speed to escape from the solar system again.

The origin of such comets is not known for certain - some may have come from other star systems. Some comets can enter the solar system on parabolic orbits - these have come from a long way out - perhaps the Oort cloud - and are just bound to the solar system. But interactions with other planets and the Sun can result in them gaining energy and leaving the solar system on unbound hyperbolic orbits.