You can see an example of what the rule is referring to over here (for yellow at least). While this particular use of old save data is obviously very easy to catch, in general this isn't something we want to leave open for people to exploit in more subtle ways, so I've chosen to make this rule explicit.Having a save file present on the cart/emulator when you start the run is not allowed. This rule is in place to prevent carrying over certain parts of save data from the old file, such as the glitched "fastest" text speed. You can use Up+B+Select on the title screen to clear your save data.
Note: This doesn't (currently) apply for gen2 games onwards, using old save data for those games to speed up resets is still allowed. This only applies for all the Generation 1 games/categories as of writing.