In digital photography, the cloning tool is used to copy one part of the image into another area, or even into another picture entirely. If your beautiful picture of clouds at sunset is ruined by the ugly electrical wires running across them, it can be fixed. The wires can be painted right out of the picture by using the cloning tool to copy small bits of the clouds around the wires over top of them.
This technique can be time-consuming, especially if there is a large area that needs work. It is also very easy to do it badly, with results that clearly look like they were cloned. Remember to click on different areas of the picture to be the source of the cloning tool, because if you don't, you can easily get a tell-tale pattern in the texture of the image.
Cloning is also useful in other ways. Imagine two pictures of the same family portrait. In the first, Grandpa is yawning. The photographer saw that, and shot a second one, but he didn't notice Junior sticking his tongue at his sister in the second shot. Rather than throw away both pictures, the photo editor can take the smiling Junior from the first image, and clone it over the ugly one in the second photo.
Cloning is one of the most common tools used in photo faking, just as the family portrait example shows. One recent example is Lebanese photographer Adnan Hajj, who was fired by Reuters. He was caught using a cloning technique on his pictures, making battle damage in the 2006 Israel-Lebanon conflict look much worse than it really was.