Being an apprentice
graphic designer, I think I'll take a shot at this one.
In the early days of the typewriter, every letter was the same size. It was all like this.
If I type some more bla bla bla bla bla you'll begin to see (actually it's hard to see on a computer screen, but find some old typewritten text or something and look at it) that often times the spaces between letters and words line up creating what's called "rivers" running down the page.
This can get distracting and cause the eye to just "skip over" bits of text.
If you read a really long document, before long you would find yourself unconciously running sentences together as you missed periods.
To stop this, writers started putting two spaces after periods to "break things up".
This caught on and became the accepted standard. Then came word processors with their pretty non-monospaced fonts. You'll notice that there are no "rivers" in normal computer text, because the letters are different sizes. The eye can read them more easily.
However, a lot of typers still put two spaces after periods, which tends to just look dumb with a nice font. The computer is not a typewriter.
There is some evidence that this is why HTML does not allow multiple spaces. (to do that anyway, type wherever you want a space.)