MetaFont was written by Knuth as a companion to TeX; whereas TeX defines the layout of glyphs on a page, MetaFont defines the shapes of the glyphs and the relations between them. MetaFont details the sizes of glyphs, for TeX’s benefit, and creates bitmaps that may be used to represent the glyphs, for the benefit of programs that will produce printed output as post processes after a run of TeX.
MetaFont’s language for defining fonts permits the expression of several classes of things: first (of course), the simple geometry of the glyphs; second, the properties of the print engine for which the output is intended; and third, ‘meta’-information which can distinguish different design sizes of the same font, or the difference between two fonts that belong to the same (or related) families.
Knuth (and others) have designed a fair range of fonts using MetaFont, but font design using MetaFont is much more of a minority skill (even) than is TeX macro-writing. What is more, it is a dying art: few new TeX-related fonts are produced using MetaFont, nowadays. Indeed, several of the major font families (that originated in MetaFont designs) are now seldom used in any other way than their conversion to an outline font format.
This answer last edited: 2011-07-03