Just listening to podcasts will still use up RAM that isn't released until the OS decides that it's time to do so. There are also a lot of other little processes going on the background that can allocate resources over time.
There is absolutely no calibration going on.
There is a digital input on an IC inside the phone that monitors the voltage on the home button input line. That line is normally held to a high voltage through a very small resistor that is part of the circuit. When you press the home button, the input line is shorted through the button contacts to ground. The small resistor ensures that the short circuit behaves in a predictable manner. There are two states that the home button input line can be - high or low (ground).
When you press this button, you are not interrupting anything like turning off a light switch. You are just letting the computer know that you pressed the button. At that point, the computer says to itself, "Hey, somebody pressed my home button. I should do something about that as soon as I get a chance."
As soon as that happens, the OS starts to go through its process for dealing with a home button press. If the application that is open needs to stay resident in RAM or run in the background, it will start copying the necessary data into the proper RAM while exiting the app out and returning to the home screen. If you have a lot of free RAM, this appears to happen almost instantly. You're back on the home screen, but the exited app is still likely doing stuff in the background for several more seconds. The way that multitasking works on iOS means that nearly everything goes into RAM when you press the home button.
If you have filled up your RAM, iOS will look at all of the apps that are using up RAM and decide which ones are the best candidate for getting kicked off of the bus. Before it evicts it, though, it lets each app do its own cleanup BEFORE it exits the current app, like saving things to the disk or cloud. As soon as the old apps are finished taking care of their cleanup tasks, the OS goes back the the home screen and begins moving all the new (just closed) app's data into the RAM holding area. This is what makes the home button seem unresponsive.
"Calibrating" the button frees RAM, and free RAM makes the home button's background tasks much quicker.