The Birdeye View shows the whole map in a small scale and gives you an overview over the area you have explored so far.
You can leave the window with the birdeye view open during your turn. When you click into the window with the mouse, your main window will display the area around the point which you have selected in the birdeye view.
You can open or close the birdeye view with the button "Game" : "Map".
Never close the birdeye view directly from your window manager!