Contrary to what you may think, clearing or swiping away apps in the Recent Apps view on your Android device does not necessarily stop app activity or running tasks—and these running processes can actually be eating away at your battery life. Depending on the app or process, it may only be a small percentage, but every little bit helps these days.
In order to ensure that you're actually killing an app and its background activity, install ShutApp from YirgaLAB. This app not only hault running background processes, it also displays the potential data and battery life saved by doing so.
When you first open ShutApp, you'll be required to enable accessibility services for it. Tap Open Service, then locate ShutApp under the Services header and toggle it on.
Whitelisting certain apps will prevent ShutApp from killing them. You should whitelist things like live wallpapers and music services—basically anything that you want to persist. Just enter the whitelist through the settings, select an application, then hit Add.
Tap the large SHUT button to begin killing apps, after which you'll see a Done screen with information on how much battery and network data was saved.