• It orbits the sun, not another body.
• It has enough mass that its own gravity molds it into a spherical or near-spherical shape.
• It has cleared large objects out of its path (large objects will either collide with it, or be hurled away from it).

Based on these rules, it is easy to see why, for example, the moon is not considered a planet, even though it is large enough to be spherical; it orbits the Earth instead of the sun.

Similarly, we can see that the asteroids of the asteroid belt aren't classified as planets, even though they orbit the sun. They aren't massive enough to be spherical in shape.

But what about Dwarf Planets? What are they? Dwarf Planets are objects which satisfy the first two rules above, but not the third one. Thus, though Pluto orbits the sun, and it is massive enough for its own gravity to shape it into a sphere, it has not cleared large objects (like Charon) out of its path. Thus, it is a Dwarf Planet, rather than a planet.