‘Standard profile' refers to the height required to push your key switch (button) down to register a press. This is opposed to ‘low-profile’ key switches which I prefer.
This video has a good overview: Why Switches might not be optimal for Super Smash Brothers Melee!. TLDR: the high actuation points of non-low-profile switches may not lend itself well to melee, particularly when trying to quickly release an input (shorthopping is hard on standard-profile).