A measure of how circular the orbit of a planet is.
The orbits of the planets are not perfect circles: they are ellipses. They are like slightly squashed circles. The eccentricity is a measure of how perfectly circular they are: a eccentricity of 0 indicates a perfect circle. More elongated ellipses have eccentricities with high values, up to (but not including) 1.
The eccentricity of the Earth’s orbit is 0.0167, which means it’s almost perfectly circular. The widest part of its orbit is about 300 million kilometres from one end to the other. The narrowest part is only about 26,000 km less than this – that’s only about two Earth diameters.
(This does not mean that the distance between the Earth and the Sun only varies by about two Earth diameters during its orbit. This is because the centre of the orbit is not in the same place as the centre of the ellipse. See aphelion and perihelion for more details.)
The most eccentric orbit of the planets is that of Mercury, at 0.21. Pluto, which is a dwarf planet, has an orbit so eccentric that it actually crosses the orbit of Neptune — so sometimes Pluto is nearer to the Sun than Neptune is. This was last true between 1979 and 1999; but it will not be true again for over 200 years.
Comets tend to have highly elliptical orbits. For example, Halley’s comet has an eccentricity of 0.967. (Neptune’s eccentricity is 0.00859, which makes its orbit even more circular than the Earth’s.)