A: The saturation current is essentially a measure of the maximum possible current that can flow - in this case, measured as the rate of flow of photoelectrons. An increase in this saturation current implies that this rate of flow of photoelectrons has increased, and that can only happen if one were to allow more photoelectrons to pass in unit time.
Now, this is where we have to remind ourselves where these photoelectrons are coming from: it’s all a consequence of the photoelectric effect, wherein photons of electromagnetic radiation strike the surface electrons, allowing them to escape entirely. So if you’re seeing more photoelectrons flowing in a given unit of time, then that means you have more photons striking the metal. That can only happen if you were to increase the intensity of the source of electromagnetic radiation - i.e. increase the number of photons emitting per unit time.
So putting two and two together, the one parameter causing this increase in saturation current is intensity!
