The clone tool is selected with the rubber stamp icon in the toolbar (in some software packages it is called 'rubber stamp').
It can be used to remove unwanted parts of an image or to add parts in.
All it does is copy one part of an image to another.
First choose a suitable size brush, almost certainly a soft one.
Hold the alt key down and click on the part of the image you want to copy from.
Then, use the brush to paint in the copy.
The Eiffel Tower picture is from a digital camera and had the date imprinted on it. It can very easily be removed by copying a section of sky, from just to its left, over the date. The parts of the picture are not very different and with a soft brush it is almost impossible to see the join.
One of the main uses of this is to remove dust specs and other faults from images. Use it also to remove creases from old photos and those lamp-posts that stick out of people's heads.
Conversely it can be used to add to an image as in the case of the 'twins' above. Add a few birds in the sky, an extra tree on the horizon. It can be used to copy from one picture to another. I've seen it used improve a picture where one of the people had blinked. A pair of open eyes was cloned from another picture!