Force stop app
The Force stop function for an app within the Apps settings stops the app from running, if it is currently running. If the app is doing something in the background, that activity will be stopped immediately without waiting for it to finish. The app may still be used as normal afterwards by starting it in the usual way.
This action is also commonly known as "killing" an app.
How it works
In Android it is standard for apps to remain resident in the device's memory when you switch to a different app, such that returning to the app later is a fast and responsive operation. However, in most cases while in the background the memory it occupies is marked "discardable", meaning that it can be wiped and re-used at will by Android should another app require it, because the app has already saved any important state information to permanent storage.
Thus, it's not necessary to force stop or "kill" an app to free memory, as Android will free its memory when needed.
Force stopping an app removes it regardless of its current state, and there is a possibility of losing any unsaved data in the app when using this option, even though the design of Android tries to ensure that any important permanent state information should already have been saved.
While there should usually be no reason to force stop an app, this action is useful if an app has a bug or malfunction causing it to be unresponsive or to become stuck performing a background task that is taking a long time or never ending.
Force stopping an app can also save battery life in cases where a background app has become stuck in an endless loop or doing an excessive amount of processing in the background, and the app is not responding to requests to stop.