Holy guacamole, I can actually answer this one. But first we have to go back to mainframes...

Back in the days of yore, desktop computers weren't a thing. Instead, you'd have a keyboard and monitor connected to a terminal of one sort or another. There were two main categories: character-oriented terminals and block (or data stream)-oriented terminals. The former was cheaper to make due to the smaller component count and simply transmitted each keypress to the connected mainframe or (later on) minicomputer.

Block-oriented terminals were an interesting development. In exchange for adding a bit more circuitry to each terminal, the demands on a mainframe's time could be decreased. For example, consider an airline ticketing system. A booking agent wants to search for flights from JFK to SFO, deparing on 7/5/74. A character-oriented terminal would interrupt the mainframe each time a character was pressed, leading to expensive context switches as the mainframe had to service requests from each active terminal. A block-oriented terminal would be able to present a form with fillable fields for origin, destination, and date, which would only interrupt the mainframe when all data was submitted at once. IBM was able to take advantage of this to allow a single mainframe to serve a massive amount of terminals, but this meant that any interaction represented a relatively significant expense as compared to character-oriented terminals. (Consider the case of typing a paragraph of text and saving it. On a character-oriented terminal, the "save" command would be just one interrupt, after the interrupts for each letter. On a block-oriented terminal, the "save" command would be the only interrupt.)

This meant it was to IBM's benefit to be able to accomplish tasks with as few interactions as possible. Interactive time-sharing applications of the time such as ISPF could present menus, but navigating a hierarchical menu meant the mainframe would have to do more work. The solution was shortcut keys. Depending on context, a mainframe's numbered PF keys would accomplish different tasks. A user would memorize the ones they used most frequently, while common shortcuts could be displayed at the bottom of the screen, both resulting in fewer interrupts for the mainframe.

How did we get from mainframes to PCs? When the original IBM PC launched, it had 10 function keys in a bank on one side of the keyboard. PCs didn't have time-sharing capabilities, and each keystroke generated an interrupt, but users still enjoyed the ability to streamline frequent tasks when supported by a given application. A subsequent model, the PC/AT, contained a standard keyboard layout with exactly half of the 24 function keys that were common on 3270-series terminals of the time, arranged in one bank rather than two. ETA: As /u/OnlyDeanCanLayEggs notes below, this particular keyboard is sufficiently well-known that its model name, "Model M", is still widely recognized today.

Edit: Terminology.