Eccentricity
Eccentricity: how much a conic section (a circle, ellipse, parabola or hyperbola)
varies from being circular.
A circle has an eccentricity of zero, so the eccentricity shows you how "uncircular" the curve is. Bigger eccentricities are less curved.
Different values of eccentricity make different curves:
 At eccentricity = 0 we get a circle
 for 0 < eccentricity < 1 we get an ellipse
 for eccentricity = 1 we get a parabola
 for eccentricity > 1 we get a hyperbola
 for infinite eccentricity we get a line
Eccentricity is often shown as the letter e (don't confuse this with Euler's number "e", they are totally different)
Animation
Try the slider to see what happens:
Calculating The Value
For a circle, eccentricity is 0  
For an ellipse, eccentricity is: 

For a parabola, eccentricity is 1  
For a hyperbola, eccentricity is: 