On a typewriter, all characters are monospaced; each letter takes up the same amount of space—the letter "i" takes up as much space as the letter "m" and a period takes up the same amount of space as a capital "W." Because all characters are monospaced, the tradition was to type two spaces after periods to separate sentences.
Computers use fonts that are proportional, each character taking up a proportional amount of space—a typical letter "i" takes up about one-fifth the space of the letter "m." So you no longer need extra spaces to separate sentences. Pull down any book on your shelf—you won't find two spaces between sentences. We don't need the extra space to tell us when a new sentence has started. With the creation of fonts and computers, the extra space is actually distracting.
Yes, this is a difficult habit to break, but it must be done. If you don't believe me (or my sources in graphic design training), check with the "goddesses of all things editorial" The Chicago Manual of Style.
[There are a couple fonts (Courier and Monaco) that were created to resemble typewriter quality and are still created monospaced; but they are few in number and not very pleasant looking.]
Most of this is paraphrased from The Mac is Not a Typewriter by Robin Williams