What is the Widget z-index?

The widget z-index is set in the Widget Editor for the respective widget. You start in the widget overview, select the respective widget and then navigate to the "Appearance" tab.
The z-index specifies the order of an element in relation to other elements on a page. Elements with a lager z-index overlap those with a smaller one. By default, the Widget's z-index is set to its maximum value, so no elements cover it.