METAFONT is a font description language designed by Donald E. Knuth. It is practically the sister program of TeX, and TeX uses METAFONT fonts natively (though some macro packages, such as LaTeX, allow the use of PostScript fonts). It all started from the Art of Computer Programming series: Knuth didn't like the typography in those books, so he designed a new typesetting system (TeX) to lay out the letters, and new font description format (METAFONT) to get beautiful letters. I hope he will finish the fourth volume of the Book one day, after spending decades on fixing little bugs...
METAFONT program (whose current version number is 2.7182 - when the version number of TeX approaches π, METAFONT's version number approaches e) produces two things for TeX use: the font metrics file (*.tfm), that tells what size the glyphs are, and the bitmaps of the fonts for display at specific resolution (*.gf, "general font", usually compressed to *.pk).
METAFONT, like TeX, is "frozen" and will only be bugfixed in the future - and, honest, it's as good as it can get, and TeX is still a wonderful system to build typesetting applications on.
As in case of TeX, Knuth pays for bugs that are found from the code and reward doubles every time a bug is found. But don't count on anything - apparently the last unlucky bug was squished in January 4, 1986.
METAFONT is actually a full-blown declarative programming language, and each "program" produces a whole family of fonts. In this respect it clearly smokes Adobe's Type 1, and still leaves TrueType gasping for air a bit. It is also based on macro libraries. METAFONT is rarely invoked by the user, because it is usually automagically called by TeX to produce required font files.
The usage of the program is described in The METAFONTBook by Donald E. Knuth (Addison-Wesley 1986, ISBN 0-201-13445-4). The book (which I haven't seen) had this very interesting warning that, in my opinion, tells what the art of anything is really about:
Warning: Type design can be hazardous to your other interests. Once you get hooked, you will develop intense feelings about letterforms; the medium will intrude on the messages that you read. And you will perpetually be thinking of improvements to the fonts that you see everywhere, especially those of your own design.
...I have had similar feelings regarding other forms of art that I have practised =)
See also: TeX, MetaPost