Please forgive me if this sounds insulting, I just don't know the extent of your experience.
You have two type of powered devices on board, 12v DC and 120v AC. When plugged in or have the genny running, you have 120v AC powered to the panel. That will power any 120v items. Those will include your Air Conditioning and anything that is plugged into a standard 120v wall socket. As was mentioned, originally the fridge was a 12v/120v convertable so it would run on either. Unless you have a propane stove, that too will require 120v AC to run.
Many boats have an inverter. This converts your battery 12v DC to 120v AC. This is great for running small loads, or short term loads (such as a fan, iphone charger, coffee maker) but won't handle big loads or you will quickly drain your batteries.
So, if you had the boat surveyed before you bought it, the survey will show if you have an inverter or not. If you didn't have it surveyed, then you need to start hunting around the boat to see what you have.