It's called the App Shelf. It can be manually triggered by tapping the three dots at the top center of the screen. It appears automatically whenever you open an app where you have multiple windows open, as demonstrated by your screenshot.
To my knowledge there is no specific option available to disable the App Shelf or multi-window support (which would also negate the need for the App Shelf).
You can however stop the App Shelf from appearing automatically by closing all but one of the app's windows, and using tabs instead (in the case of Safari). Looking at your screenshot, you could close the "philo.com" and "Start page" windows (you can' close the currently active one, as indicated by the white border).
To close a window from the App Shelf, simply flick it upwards. You can also close windows from the multitasking view the same way.