Two spaces after a period is an old typing practice. I remember being taught to do this in High School typing class. But what do the experts have to say on the subject? Here’s Robert Bringhurst in The Elements of Typographic Style1.

In the nineteenth century, which was a dark and inflationary age in typography and type design, many compositors were encouraged to stuff extra space between sentences. Generations of twentieth-century typists were then taught to do the same, by hitting the spacebar twice after every period. Your typing as well as your typesetting will benefit from unlearning this quaint Victorian habit. As a general rule, no more than a single space is required after a period, a colon or any other mark of punctuation.2