That's the pop-up view option. Unfortunately, you can turn off the gesture to activate it (probably what's causing you to minimize apps like this) but you can't turn it off entirely. If you have two apps running at the same time, you can still pop-out the app (as long as the app supports it) and make it a floating window. Furthermore, once the app is 'floating', you can minimize it, causing the floating icon you see now.
The gesture you can turn off is to swipe diagonally from any of the top corners into the opposite corner below; that would cause the app to become a floating, resizable window which can then be minimized into the floating icon you see (again, not all apps support this). To do so, go into your phone's settings, then Advanced Features, then Multi-Window and turn off the Pop-up View Gesture.