smartthinking, Peggie's probably correct on all counts. It sounds like the tank next to the toilet is the toilet waste holding tank. The manual pump next to it is most likely a manual bilge pump that is used to empty the holding tank when out to sea. It should connect to the bottom of the tank, and at the other end, to a through-hull fitting. You open the seacock at the through-hull fitting, then pump the pump to empty the tank out into the water. Note: you can only do this legally if you are 3 miles or more out in the ocean. You cannot do it in coastal waters or in any lake or river - only 3 miles or more out in the ocean. There's a hefty fine if you get caught...
The bung on the deck, marked "Waste" is the access for pumpout of the tank, either at a dockside facility or via a pumpout boat. There should also be another (smaller diameter) hose coming off the tank that goes to a vent through-hull fitting on the side of the hull, usually up near the toe rail. This vent must be clear at all times, so that air can come into the tank when it is being pumped out, and air can escape from the tank as it fills. If this line becomes plugged-up, you won't be able to have the tank pumped out, and you will have difficulty flushing the toilet. If the air cannot escape from the tank as it fills, the air will compress inside the tank, pressurizing the tank. This will cause the toilet to not flush properly, and could cause the toilet to back up. It can also cause a "brown guyser" to erupt from the deck fitting when you remove it. When loosening the "waste" cap, do it very gingerly - if it starts to hiss as you loosen it, STOP and wait until the pressure relieves itself before continuing.
As Peggie and others have mentioned, you should crawl around the boat and find and discover every single component on the boat and determine what it does and why it's there. Then, when problems develop - and they will every now and then - you'll know where to look, and what to look for. Marine plumbers depending on where you are, charge anywhere from $50.00/hr. to $150.00 per hour. So the more you understand your onboard systems, and the less you have to call them in, the better off you are.