The ratio of the distances between a point on a conic and a fixed point (the focus) and between the point and a fixed line (the directrix). For e = 0 a circle is produced, for 01 the conic produced is a hyperbola.
Conics of different eccentricities
http://www.math.odu.edu/cbii/calcanim/#defel
• Two animations of ellipses with different eccentricities.