Dwarf planets are objects in the solar system which orbit the Sun. They are large enough that their gravity has caused them to form a spherical shape. Unlike planets, they have not cleared their orbits, meaning that there could be several or many dwarf planets orbiting the Sun at the same distance and in the same plane. Satellites of planets are not considered dwarf planets.
The dwarf planet Pluto taken by NASA's New Horizon's spacecraft in 2015. Source: NASA/ John Hopkins University Applied Physics Laboratory/ Southwest Research Institute/ Alex Parker
The definition of a dwarf planet was agreed upon in 2006 by the International Astronomical Union (IAU) after being debated for years. Pluto had been considered a planet for several generations, but in 1992, other objects were discovered in the same region as Pluto, and then in 2003, Eris was discovered, and found to be larger than Pluto. Astronomers realized that more and more objects were being discovered beyond Neptune in the region known as the Kuiper belt, and that if Pluto was going to be considered a planet, many (possibly hundreds of) other objects were going to be added to the number of planets in the solar system. Instead, the IAU decided to create a new category with Pluto as the first member. At the moment, there at least 5 confirmed dwarf planets and many more candidates.
When the definition of dwarf planets was agreed upon, the largest member of the asteroid belt, Ceres, also qualified as a dwarf planet.
Largest known Kuiper Belt Objects. Image credit: ESA