I also agree the button is for sea water and I will assume there is a pump in the base of the head.
If it's just a single button, your toilet is one that has an integral intake impeller and discharge impeller that simultaneously bring in sea water and push bowl contents out. Most likely it's a Jabsco 37010 You'll find the owners manual here:
Jabsco 37010 owners manual If it's not that one, it has to be a Raritan SeaEra:
Raritan SeaEra owners manual