A critical function is a function of the software that will not execute on all players. It can be hoped that in the future all vendors of Wherigo players find the time to correct the implementation of the critical functions but for the time being different players react differently to some Wherigo functionality.
If you look at the opening statement for this section you will see that actually the function as such is not critical but using the function will be critical because the resulting cartridge will not work on some players (you are typically loosing 50% of the installed base if you use critical functions).
Function in this context does not refer to a function call in the Lua software. It is used as a general description for “something” that the software provides for. Anything can be a function in this context.
Some guidance how to avoid known issue can be found in the Tips and Tricks (How to make sure your cartridge works for all players) section of this Wiki.