A circular orbit is type of orbit in which a celestial body moves in a circle around another celestial body. While drawings of objects in orbit often depict these objects in a circular orbit for reasons of simplicity, circular orbits are actually quite rare, requiring a sort of perfect storm of circumstances to occur. In our solar system, the Earth comes the closest to having a circular orbit, which is one of the reasons it is habitable, and among the planets, Mercury has the least circular orbit. (Now that Pluto has been downgraded, it no longer holds the “most eccentric orbit” title.)
Celestial bodies tend to orbit in an ellipse, with the object they are orbiting around at one of the focal points of the ellipse. The ellipse can be very stretched out and elongated, or closer to a circle, with the term “eccentricity” being used to describe the shape of the ellipse. An orbit with an eccentricity of zero is a circular orbit, while an orbit with an eccentricity of one would be highly elongated. Just for reference, the eccentricity of Earth's orbit is .0167.
In order for a circular orbit to occur, the orbiting object has to achieve the right velocity, and the interaction between the object in orbit and the object it is orbiting around must remain stable. This is fairly rare; satellites launched from Earth, for example, usually have a more elliptical orbit because it is difficult to get them to fall into a perfectly circular orbit.
A number of calculations can be used to determine the eccentricity of an orbit, and to play with variables which could change the shape of the object's orbit. These calculations can be used to analyze data about objects in other solar systems, and in the development of mission plans for satellites and other objects being launched from Earth.
The eccentricity of an object's orbit can have some interesting implications. For Earth, the slight shifts in position relative to the Sun play a role in the seasons, but the fact that the Earth's orbit is close to circular in nature also prevents extremes. If Earth had a more eccentric orbit, the temperature swings between seasons could be too intense for organisms to adapt, making it impossible for life on Earth to occur. Differences in orbit also explain why sometimes various celestial objects come into alignment with each other, and at other times, they do not.