A monsoonshield is mounted above the doors of some automobiles, to protect the inside of the car from rain or other precipitation in case of slightly opened windows. Additionally, it may help to prevent precipitation entering the interior in case of an opened door, eg. dropping from the roof or directly from the air.
However, in most of the cases they are probably installed for better outward appearance of the vehicle. They tend to be easily broken, if made from weak materials and the passengers do not take care when entering or leaving the vehicle.
It is also known as a rain visor (in countries without monsoon).