What Aimee said.
It used to be two because typwriters give every character (be it a period, letter m, a comma, or a space) the same exact amount of space. By using two spaces after a period, it will emphasize a new sentence and not confuse the reader to think it was just a comma.
With today's word processing software and updated fonts, space for each character is dependent upon the character itself. A small letter i will take up less space than an m. These type of fonts are easier to read, so a double space after a sentence is no longer necessary.
Still, it is ingrained in most of us (those who grew up with typewriters) to continue to use two spaces after a period, although it is not necessary anymore. It isn't INCORRECT, it just isn't necessary.
Did you win the argument?