What does left clicking in the 3D view do? I don't understand what the white circle with the cross is for. I can change its position by left mouse click in the 3D view. Why does it change its position and what it is for?
This is the 3D Cursor, and is useful for several things in advanced editing. When you left-click you are setting the position in 3D space for it to be. It works in all modes.

If you would like some more details, go to the Blender Manual.