The Action of a whole program is very easy to understand. A tax program "does taxes." A calculator program "does math."
An Action is always a verb of some sort. "Calculates." "Fixes." "Adds." "Removes." Those are actions. Usually they're a little more descriptive and specific, though, like, "Calculates how much rainfall there will be in Africa next year," or "Fixes broken hard drives."
Inside of a class, the Action is the code inside of the methods. That's all some sort of action – something going on, something happening. In many programming languages, you can also have code outside of any class or function – code that just runs when you start the program. That's Action.