Printing-press typesetters had a rule for how much space should be between sentences. Then people started having personal typewriters that were monospace, so to make their documents look similar to traditional publications and to more easily see the punctuation marks, people would put two spaces before starting a new sentence. Personal typewriters got more sophisticated with better spacing, making double-spacing unnecessary, and then computers came on the scene with word processing software, which also had no need for the improvised double-spacing.

But people had already learned from their teachers back in high school that they should double-space on the typewriter. So they taught it to their students with advanced typewriters and computers, and some of those students to this day just won't quit.

Typewriters were/are monospaced, so putting a double space after the full-stop helped you recognise the start of a new sentence, giving it, and you, breathing space.

The PC fonts are size adjusted and double space is no longer necessary, but it doesn't hurt.