The IAU determines what makes a planet and essentially the arguments for Pluto being a planet rather than dwarf planet are emotional rather than scientific. Just because you really really want money to grow on trees doesn't mean that we should classify it as a plant.
Pluto is a strange and very important body because of how distinct it is. As you can see in the above animation, Pluto and Charon form a double planet system where they each orbit around a common point between them rather than a simple orbit like the Moon has to the Earth. Well, the Moon doesn't actually orbit the Earth but instead a common point of orbit that both the Earth and Moon go around. This common point just happens to be inside the Earth, more info here for the intrigued.
As the barycenter of Pluto and Charon is actually outside of Pluto then they form a strange double dwarf planet system. Pluto is in a place called the Kuiper Belt which is where all of the rocks that formed the planets in the Solar System originally are left. The ones more inner than this were swept up by the planets as they were going round the Sun like a space hoovering system.
Pluto is amongst the largest we've found in that belt but there are tens of thousands of things that we could call a planet if we call Pluto a planet. Instead most refer to it now as a Plutoid, a new type of large dwarf planet.
One of the very interesting things is that people are starting to consider the idea that Pluto may form its own system out there where it has lots and lots of Moons.
Unfortunately after a 10 year journey, New Horizons will be taking its best photos just for a single day as then it will be moving away from Pluto