When we speak of deleting a selection, what we really mean is the deletion of the image region bounded by the selection. If you just want to delete the selection border, use the Deselect feature.

 

To delete the selected part of an image, make your selection, and then hit either the Delete, or Backspace key.

 

Here is an image with an oddly shaped selection.

 

 

The picture that follows shows the same image canvas after pressing the Delete key.

 

 

 You can see that the selected region has indeed been deleted. If you wish, the deleted part can be recovered by deleting the Clear item from the history palette (drag it to the trash can icon in the lower right).

 

Removing the Clear item from the history palette will restore the missing region and delete any image states from the Clear item down to the bottom of the list.