What is the Definition of a Dwarf Planet?
When the IAU decided to create this new classification, they defined it by comparing it to planets. In the same assembly, a new definition for planets was created. A planet is an object that is a) orbiting the sun, b) is massive enough so that its gravity has crushed it into a roughly spherical shape, and c) has cleared the neighborhood around its orbit.
A dwarf planet is an object that fulfills only the first two criteria for a planet, but has not eaten up all the debris that is around it. This creates a new type of object that is different from moons or satellites or the irregularly shaped asteroids.
In 2006 the IAU only named three dwarf planets: Pluto, an asteroid named Ceres, and a new object in the Kuiper Belt temporarily named UB313. By 2008, the IAU has named a total of 5 dwarf planets: Pluto, Ceres, Eris, Makemake, and Haumea. The important thing to remember is that the International Astrnomical Union had no malicious intent when they "demoted" Pluto. Some people take it as an affront to the feeling of wonder they had as children, learning about our solar system and Pluto, the runt of the litter. Just remember, Pluto is in a better place now. It can finally feel at home, floating through space with its brethren.