While general purpose function keys are something that had already been introduced in the 60s by manufacturers like Friden (Flexowriter, 1965) or HP (9810A, 1971), it wasn't until IBM's 3270 that function keys were widely available. 3270 terminals are block-orientated, which means all keystrokes, thus all editing, are local. Only the whole screen can be sent back (*1). The PF (and PA) keys are an exception to this as they deliver short predefined messages directly to the mainframe (*2), allowing the (mainframe) program to respond directly to such a request.
When CICS (developed in the late 60s) added 3270 support (~1974), a help utility was added and by convention activated via PF1. Due to the asynchronous nature of PF key messages this enabled the addition of help information/screens to an existing application without modifying it (*3). Using PF1 became the de facto standard for mainframe applications, not just with IBM and CICS.
When the PC became available, many professional programs did follow the same practice, but it wasn't until 1987 when IBM published their Common User Access (CUA) guidelines as part of the Systems Application Architecture (SAA) standards, that F1 as Help became the 'official' standard.
*1 - Well, not entirely true as a terminal can be ordered to send back either the whole screen, all fields, only modified fields, or marked regions. But that's part of the high art of block terminal programming.
*2 - Sending a message to the host - no matter if it's a full screen or a function key - always generates an input interrupt requesting attention and delivering the data (when served). A
PF key delivers only two bytes of information (plus some header) which makes transmission, moving and handling way faster than a whole screen.
*3 - CICS is a Transaction Monitor, something that PC developers might call an application framework - or a program/window manager, or even an operating system. It offers a backbone structure where individual programs are 'just' function modules loaded into this framework and executed upon messages from the monitor program - like incoming screen (user input), network messages, lost connection or the like. In fact, they might only get loaded on demand and unloaded after handling such a message.
Much like a window manager can handle certain UI functionality without activating a user program, CICS can offer to handle (some) function keys without activating any user module. Doing help screens is one of these offers.