What the Facebook app does actually is the basic default behavior of Android. Those apps don't do anything special regarding that behavior. The Activity stack is saved by default.
One of the more cited blogs regarding it is CommonsWare's BACK means Back. Basically, the functionality of the "BACK" button means it should to take you to the previous page that you just were at. In Android, this is very often the last Activity you just pushed. If the user wants to leave the app, then he or she can press the "HOME" button and that will always push the Activity stack and take the user to the homescreen.
What this means is, the functionality of the BACK button is entirely dependent on the app in question, but the concept is to reverse the action that the user just did. If you are in a game, you go to a sub menu, the BACK button should take you to the top menu. If you are in a browser, the BACK button may take you to the last webpage you were viewing. If you are in a browser and you are in the top page, the user may expect the BACK button to close the app since the last action the user did prior to opening the browser is open the app. If the user starts a download, the BACK button may be to cancel it.
One functionality improvement that Facebook and others like is may consider is to wipe the stack after x number of days since the user may not remember exactly what they did since being interrupted from the last use. The use case for this is very small though.
Overall, this is why people always stress usability testing. You have to figure out what 99% of the people of the app expected when they press the back button.