A century ago Remington, Royal and Underwood were all famous brands of what? Razors, watches, hats or typewriters. All of these companies were famous for producing typewriters which were invented in the 1800s.
Back in the day when those typewriters were widely used around the world, people were taught to put two spaces in between sentences. So after you hit the period key you'd hit the spacebar twice. Here's why. Each letter printed from a typewriter took up the same amount of space, so adding the extra space after a sentence made the transition between sentences easier to read. Today though, the letters and most of the fonts we read or print have different widths. An "E" for example takes up more space than an "I". This is also intended to make text easier to read so some argue that the extra space at the end of a sentence isn't necessary anymore and several style guides from MLA to AP to the U.S. Government Printing Office suggest using only one space after a period.
But if you're old school or you were taught to use two spaces or you just like it that way, Microsoft will attack you. The company's newest version of Word will put one of those blue, squiggly lines indicating you've made a mistake after each double space following a period. Of course you could tell Word to ignore it or just turn the feature off but who would have thought there'd be a war over spacing in the typewriter space.