Elaborating on @xenoid's comment:
What a path is
What you see in your second screenshot, shown as circles joined by lines, is a path. Paths can be used for a lot of things, like creating reusable shapes, etc. They define a set lines that can be traced, aligned (to), exported to a vector graphic (like .svg) and used to create selections.
What a selection is
A selection is a part of a layer that can be modified. This is shown as a moving black and white outline. The easiest way to see this is the Rectangle Select Tool (upper leftmost in your toolbox).
How to use this for your problem
In order to fill your desired area, create a selection from the path. This can be done, for example when using the Paths dialog. Click on
Windows -> Dockable Dialogs -> Paths. This should give you a list of paths. Most certainly there will be only one in the list. If you are not sure that you got the right one, try toggling the visibility of the path(s) using the two checkboxes left of the path names. This works just like with layers. Right click on it and choose
Path to Selection.
Then you will have a selection that you can fill.