One of the methods used in visual effects on television and films, perhaps made most famous by Superman.
The principle is that a certain colour (traditionally blue, but I believe often orange sometimes) in the image is replaced by something else. In the case of TV weather broadcasts, the weathercaster stands in front of a small blue screen or perhaps a partially blue wall, and then a computer replaces this blue with the map. (The weathercaster has a monitor on the side of the screen so he/she can see what you can see, and therefore knows roughly where to point).
Superman had Christopher Reeve lying down (or suspended sometimes) on a blue table in front of a blue screen. So the only thing that wasn't blue was him. Therefore the entire background could be replaced with city skylines or whatever he was flying over.
One thing that broadcasters have to be careful of is that the people concerned aren't wearing any clothes that are a similar colour to the one that is to be keyed out. This can even extend to eye colour, and some weathercasters have to wear coloured contact lenses otherwise you could see the map through their eyes.
sideways said that orange is used when there's no people around, and green is used a lot. He also mentioned that Superman's uniform is blue (D'oh!) so this was probably done with green, not blue.