The mesosphere (literally middle sphere) is the third highest layer in our atmosphere, occupying the region 50 km to 80 km above the surface of the Earth, above the troposphere and stratosphere, and below the thermosphere. It is separated from the stratosphere by the stratopause and from the thermosphere by the mesopause.
Temperatures in the mesosphere drop with increasing altitude to about -100C. The mesosphere is the coldest of the atmospheric layers. In fact it is colder then Antarctica's lowest recorded temperature. It is cold enough to freeze water vapor into ice clouds. You can see these clouds if sunlight hits them after sunset. They are called Noctilucent Clouds (NLC). NLCs are most readily visible when the Sun is from 4 to 16 degrees below the horizon.
The mesosphere is also the layer in which a lot of meteors burn up while entering the Earth's atmosphere. From the Earth they are seen as shooting stars.