Sea water electric toilets have two pumps, one that pulls in flush water--typically an impeller (which is called an impeller because it "impels" liquid to go through it), but it can be an electrically operated diaphragm--and another impeller that simultaneously pulls waste out of the bowl while it pushes it down the discharge hose, with something called a macerator--essentially just a blender blade--in between 'em. As impellers become worn, they become less efficient...dry friction heat from running without any water or waste going through 'em will destroy one in as little as 1 minute.To flush, push a button installed in the wall next to it. Most sea water electric toilets draw about 15 amps/flush and use about 2 liters flush water.
There are some that are more sophisticated, have more powerful pumps and fancier flush buttons, some designed to use flush water from the boat's fresh water tank
, but that covers the bare bones basics. The most common example of the basic sea water electric toilet is the Jabsco
37010. You can read how it works and how its installed more detail in these pieces Jabsco 37010 Series Electric Toilet
and Jabsco 37010 owners manual
I'll be glad to answer any additional questions.