The dwarf planet is a planetary-mass object that is neither a planet nor a natural satellite. That is, it is in direct orbit of a star, and is massive enough for its gravity to compress it into a hydrostatically equilibrious shape (usually a spheroid), but has not cleared the neighborhood of other material around its orbit.
The term dwarf planet was adopted in 2006 as part of a three-way categorization of bodies orbiting the Sun, brought about by an increase in discoveries of objects farther away from the Sun than Neptune that rivaled Pluto in size, and finally precipitated by the discovery of an even more massive object, Eris. The exclusion of dwarf planets from the roster of planets by the IAU has been both praised and criticized; it was said to be the 'right decision' by astronomer Mike Brown, who discovered Eris and other new dwarf planets, but has been rejected by Alan Stern, who had coined the term dwarf planet in April 1991.
In order for a body to be become rounded, it must be sufficiently massive, to the point that its own gravity is the dominant force effecting it. Here, the internal pressure created by this mass would cause a surface to achieve plasticity, allowing high elevations to sink and hollows to fill in. This does not occur with smaller bodies that are less than a few km in diameter (such as asteroids), which are dominated by forces outside of their own gravity forces and tend to maintain irregular shapes.
Meanwhile, bodies that measure a few kilometers across – where their gravity is more significant but not dominant – tend to be spheroid or “potato-shaped”. The bigger the body is, the higher its internal pressure, until the pressure is sufficient to overcome its internal compressive strength and it achieves hydrostatic equilibrium. At this point, a body is as round as it can possibly be, given its rotation and tidal effects. This is the defining limit of a dwarf planet.
However, rotation can also affect the shape of a dwarf planet. If the body does not rotate, it will be a sphere. But the faster it does rotate, the more oblate or even scalene it becomes. The extreme example of this is Haumea, which is twice as long along its major axis as it is at the poles. Tidal forces also cause a body’s rotation to gradually become tidally locked, such that it always presents the same face to its companion. An extreme example of this is the Pluto-Charon system, where both bodies are tidally locked to each other.