* Gravity: The Earth is held in orbit around the sun by the sun's gravitational pull. This force is strong enough to keep the Earth moving in a circular path around the sun.
* Inertia: The Earth is also moving forward at a high speed, and this forward motion keeps it from falling into the sun. Imagine throwing a ball – it arcs through the air because of its forward motion. The Earth's motion around the sun is similar.
Plants, being on the Earth, are essentially "along for the ride" as the Earth orbits the sun.
Let me know if you have any other questions!