A font in the computer world usually corresponds to what in the world of printing on paper was called a 'typeface'; i.e. the overall shape and design of all the characters, punctuation marks, etc. In printing, a font was the term for a set of metal type in the desired typeface at a given size (measured in 'points') .
In computers, the terms have become somewhat synonomous, since on a computer, it is easy to scale character images up and down in size to the desired size, something which is obviously not possible in metal type.
The most useful form for a computer font is a bit array, for use in the pixels of a bit-mapped display or laser printer. However, a font in this form is more difficult to scale; it is thus common for fonts to be defined as a series of curves; these can automatically be turned into bit-maps at various sizes for use on displays, etc.