What constitutes a planet as a planet and who gets to make these decisions anyway?

Answer 1

The IAU has a naming board whose decisions most astronomers recognize. It is useful to have a common language after all. I have no idea how the IAU ended up being in charge, but it makes sense to me for the largest group of professional astronomers in the world to make decisions regarding the lingua franca of the trade.

The definition that was approved a week or so ago says that the object must have enough mass to have pulled itself into a spherical equilibrium shape, to be more massive than any other such object it is orbiting (this rules out moons) and to have "cleared out its orbital zone". So, something like Ceres in the asteroid belt does not qualify in spite of being pretty darn round.

Pluto ends up a dwarf planet because it has not cleared out its zone (to account for situations like Pluto's resonance orbit with Neptune orbit I think a better criteria would be some separation in 6 dimensional x,y,z, and v_x, v_y, v_z phase space makes more sense; Pluto never gets close Neptune, though I bet there is other debris out there close to Pluto's orbit.)

Answer 2

A planet bases its features on the fact that it orbits the sun while having its own rotational axis as well, an axis that determines that the body spins on its center. Planets can also have satellites that orbit the planet itself. But the main fact about planets is that they're round in their own gravitational space and do not emit their own light, at least not through chemo-thermal reactions within them.