A font is not what it once was.
Most people today use the word "font" for what a typographer would call a "typeface": that is, the visual appearance of an alphabet full of letters, designated by a name. Courier would be an example of a font in this sense: it has a name ("Courier" or maybe "Courier New" on your computer), and a certain appearance - it's wide, monospaced, has serifs, looks like it came out of a typewriter, you know.
A more technical person might tell you that a "font" is a file on your computer that can produce little pictures of letters that the computer then displays on the screen or sends to the printer. Bitmapped fonts are just collections of pre-drawn pictures of letters; A TrueType font, meanwhile, is more like a little program that can figure out how to draw you whatever size and style of letter you ask for.
But the word font, as used by printers, is a very old word; the OED first records its use in the 16th century.
The etymology is rather interesting.
Back in the day, type was made of little pieces of lead, each with one end (the face) cast into the shape of a letter. The word font may come from the same word root as foundry and other words relating to the casting of metals; even today, a place where typefaces are designed (even if they are digital) is called a foundry.
At the printer's, each typeface resided in a chest of wide flat drawers called cases, with the letters divided into little compartments in each case. When you wanted to print something in pica (12-point) Garamond, say, you would walk over to your chest of Garamond and pull out the two cases that held the size you wanted. On top of the chest was a stand that could hold these two cases, one slightly above and behind the other, so that you could reach them both easily. The upper case held the capital letters and some other less common characters; the lower case held most of your, well, lower-case letters.
This whole contraption, consisting of the upper case and lower case of a particular size of a particular typeface—this is a font.