Android by design leave apps in the background when you exit them via the home button.

Before 4.0 introduced the switcher button, and the accompanying swipe action to fully close an app, the only way to properly exit an app was to hit the back button until you exited back to the home screen.

This because the initial design of Android was less about apps and more about "activities". These were the individual parts of an app, and what enables that one app launch parts of another app to complete a user action (the most prominent likely being the share menu).

This was presented back in the day as a metaphorical stack of cards. As more user actions where taken that opened more activities, those activities would be added on top of the stack. Then as the user hit the back button he would be flipping backwards in that stack. To enable all this, Android keep apps around in RAM until it runs low, and then start to close down the oldest ones (first by waking them up and telling them to exit gracefully, then forcing them).

Thus often an app will sit in the background even though it is doing nothing.

One good way to observe this (until recently) was to run something like OSMonitor and look at CPU time of various app processes. Often they would be present but basically show no indication of actually doing anything. They would just sit there idle, waiting for user actions.