Why F1 is the default function key of the keyboard used by many applications/operative systems to show help information to the user?
Under MS-DOS, individual programs could decide what each function key meant to them, and the command line had its own actions (e.g., F3 copied to the current command prompt words from the previous command). Following the IBM Common User Access guidelines, the F1 key gradually became universally associated with Help in most early Windows programs. To this day, Microsoft Office programs running in Windows list F1 as the key for Help in the Help menu. Internet Explorer in Windows does not list this keystroke in the help menu, but still responds with a help window.
It looks like the practice originated with the IBM CUA guidelines, as @Marjan Venema noted.