I’m not so good with clarification, but I’ll do what I can if you ask.
First things first, you have to understand that as you heat a gas the pressure goes up. Heating makes the gas particles move faster, meaning it pushes out harder on the sides of it’s container. It’s kind of like those after Thanksgiving sales - as you increase the discount, the heat, you also increase the amount of force people are willing to exert to get to the discount.
The second part you need to understand will require you to look at the HSW’s picture of the cycle here. Know this: as the left piston goes up, the right piston goes down and vice versa.
Lastly, the Stirling engine is completely sealed with a gas in it, meaning that the gas can not escape.
Now, for how it works. Basically, a heat source (say a lamp) is applied to the left side of that picture. The right side has no heat source, so relatively speaking it is “cold.” Cold, in this instance, is just a lack of heat.
Well, when heat is applied the gas expands as described above. This pushes the piston down, causing work. This is the only stage of the engine that produces work.
Next, the piston is pushed back up, making the right one push down. When the heated air enters the right, cooler chamber it does the opposite of expand - it condenses. This condensed gas is then pushed with the right piston back into the left chamber, where the cycle is then repeated.
How did I do?