How do I use the Bridge tool under Loop Tools?

Hi Jann,

That could be, for instance, that those two Circles are separate Objects. Go into Object Mode, Select both Circles, CTRL+J to join them into one Object and then switch to Edit Mode.

Yeah as Spikey says, you can only connect vertices that are part of the same object.
In your case, you could add one circle, enter edit mode and add the second circle and position it accordingly. 
Adding a circle in object mode adds a new object, whereas adding a circle in edit mode will add the vertices to the selected object.

Notice the add menu in object mode, ADD > MESH > CIRCLE
And edit mode, ADD > CIRCLE
The difference, Object Mode -  add a circle of vertices as new mesh data (object), versus, Edit Mode - add a circle of vertices (to the selected object).

Also it makes a difference if those circles have been filled or not. If you add a circle and is empty, it will cause kind of a collapse in the middle, but if you fill them first, they will create a nice arch.