Spheroid

A spheroid is a "squashed sphere"

Three-dimensional spheroid wireframe model

Try different styles in this animation here:

images/poly-gl.js?mode=spheroid

A spheroid can be made by taking an ellipse and rotating it about its minor or major axis. Press play to see:

images/solid-rev.js?mode=ellipse

Oblate vs Prolate

The flatter one is oblate, the taller one is prolate (think "prolonged"):

Side-by-side comparison of a flattened oblate spheroid and an elongated prolate spheroid

Here are some more examples:

watermelon
A watermelon is like a prolate spheroid
discus
A discus is like an oblate spheroid
Planet Earth showing its slightly oblate shape
Planet Earth, our home, is squashed a little at the poles,
making it an oblate spheroid, but a very mild version of one.

Ellipsoid

An ellipsoid is the more general case of a spheroid.