In an ellipse, the major axis is the longest line running through its center and two foci passing through the widest part of the shape.

The minor axis is the line through the center of the ellipse perpendicular to the major axis.

It follows then that the semimajor and semiminor axes are half the major and minor ones, each running from the center of the ellipse to their respective points on the edge.

OK, you may say. So what's it good for?

They are useful in calculating the area and the perimeter of an ellipse. See? Look.

Area = pi(semimajor axis * semiminor axis)

and where a equals the semimajor axis and b equals the semiminor axis a simple approximate value for the perimeter is

Perimeter = (2 * pi) (sqrt(a² + b² / 2))

Which, if you are a geometry geek, is plenty.