Planets in general must be spherical objects (which excludes asteroids as they are too small to form spheres) that orbit a star (which excludes moons which orbit planets). The problem with this definition is it becomes hairy quickly. Buried in the asteroid belt is a large asteroid that meets that definition: Ceres. Ceres is round. It orbits the Sun. By that definition, it qualifies as a planet. Likewise, Pluto has several counterparts in its area of space that are round and orbit the Sun: Haumea, Makemake, and Eris come to mind. Remember that old saying "My very educated mother just served us nine pizzas"? Well, they lampshaded a big problem with that definition with the new pneumonic: "My very educated mother can't (Ceres) just serve us nine pizzas; Hundreds may eat."

Astronomers, seeing the problem with that definition, decided we needed to exclude all these new worlds. This would unfortunately exclude Pluto, but many astronomers were thinking that Pluto should have never made the cut in the first place. Pluto is weird. Unlike every other major planet in the Solar System, Pluto orbits outside the ecliptic. Its orbit doesn't align with the other planets, and for parts of Pluto's year, it's closer to the sun than Neptune. While Neptune's and Pluto's orbits don't intersect (if they did, Neptune would either fling Pluto out of the solar system or capture it, and we think Neptune has already captured another Pluto-like object in the form of Triton), Pluto does cross the sphere at Neptune's distance from the sun and orbits inside Neptune's distance for part of its orbit. And its orbit and characteristics matched other so-called Trans-Neptunian Objects pretty darn closely, and we'd already found something out there heavier than Pluto in similar situations (Eris). Any definition that includes Pluto would include potentially dozens or even HUNDREDS of other TNOs, and couldn't exclude Ceres.

So they made a definition for major planets which would cover the classical planets plus Uranus and Neptune. It wasn't enough that you be spherical. You ALSO had to have cleared your orbital. This covers the Major Eight clearly, while excluding a population of tiny worlds that could grow gargantuan if we allowed them to. While Pluto is still a planet, it's no longer a major planet like the classical 5 plus Uranus and Neptune. And excluding it makes it easier for us to keep up with.

But don't expect this is settled! We have some indications that there may be something out in the Outer Solar System that might set the debate again. There are several Kuiper Belt Objects that have orbits that suggest there's something out there 'shepparding' them and forcing them to assume set orbits that they'd not be in otherwise. Simulations suggest the possibility of a super-Earth or mini-Neptune (things not found in our Solar System but observed in others) orbiting the sun in a distant orbit. This silent, cold traveller would have a mass of between 5 and 10 Earth masses, and would be moving so slowly that it can't possibly clear its orbit like Earth or Jupiter can. Still, something between Earth's and Uranus's mass should probably be a bit more special than Pluto, so I suspect the definition will change again when and if we find this hypothetical large body in the outer solar system.