The Notes text box in the Identity Inspector allows you to add a note to a user interface element. The text box exists mainly as a convenience to you in Xcode.
The Show with selection check box means that Xcode displays notes for a user interface element when an element is selected in the canvas or object list. But nothing happened for me when I added a test note for the user interface element and selected the element. Perhaps someone else will come up with a better answer for what the checkbox does.