Unless you're a trumpet or trombone player, and are using the plunger's head for a mute, a toilet plunger has no place on a boat. NEVER use a plunger on a marine toilet, particularly a manual toilet. It won't clear it, and it may wreck the valves inside the toilet.
First step, bail as much water and "other stuff" as you can out of the toilet bowl from above. When you get down to where it is just water remaining, a cheap turkey baster from a dollar store will aid in getting the bowl empty. Next, break the connection at the rear, where the large discharge hose connects (remove the fitting with the hose attached), and clean out that area. Fair chance that it's simply a plugged-up joker valve. Then remove the discharge hose from the fitting and re-attach the fitting (and joker valve). Replace the original discharge hose with a shorter replacement, leading to a bucket. Flush the toilet. It should clear out in fairly short order. When clear water is coming out of it at the proper rate when you flush it, the toilet itself has been cleared. Then as Peggie noted, a plumber's snake through the discharge hose should be able to dislodge anything else that may be clogging it between the toilet and the tank. Don't run the snake through the toilet; run it through the discharge hose after it's been disconnected from the toilet. Finally, reconnect the discharge hose to the toilet and you should be good to go.
Electric macerating toilets are somewhat more difficult to unclog (depending on the particular make and model), but I'm guessing that this is a manual toilet.
