On all planets with an atmosphere, but especially the Earth (our usual point of reference), the stratopause is the boundary between the stratosphere and the mesosphere. In our atmosphere, slightly over 30 miles (50 km) above the surface, where the pressure is a tenth of a percent of what it is at sea level.
Just below the stratopause lies the stratosphere, which, after the troposphere, is the second of the layers of the atmosphere. In this region, which stretches from 6 to 30 miles above the surface of the Earth (and starts slightly slower in the Arctic and Antarctic), is usually a range of significant temperature changes, with warmer air in the upper levels but colder air below. This is a reverse of what happens in the lower troposphere, where lower air is warmer and higher air is colder. Commercial aircraft usually fly in the lower levels of the stratosphere to take advantage of greater fuel efficiency in the cool air, as well as the reduced frequency of turbulence.
The temperature continues to increase until the actual stratopause itself, by which time the air is a chilly but comparatively warm 30 degrees Fahrenheit (-3 degrees Celsius). Until this point, the air has been warming because of the ozone layer, which absorbs UV rays and, in the process, heats up the air around it. Above the stratosphere, the ozone layer thins out again, and as a result, the temperature again begins to fall.
The mesosphere continues from the stratopause to about 50 miles above the surface of the Earth (or 85 km). It is marked by another boundary, the mesopoause, followed by another layer, the thermosphere. Throughout the mesosphere, temperatures begin to fall from the peak reached at the stratopause. Temperatures can drop as much as 180 degrees Fahrenheit (100 degrees Celsius) from the peak reached in the stratopause.
The mesosphere also features such unusual phenomena as a layer of sodium ions (which helps cause the vague glow of the atmosphere at night), and atmospheric tides, caused by the planet's gravity, which help drive air around the planet. Unlike the stratosphere, the mesosphere is generally inaccessible for jet aircraft, but it is still well below the altitudes necessary for orbital space travel. For this reason, it is arguably one of the less well understood areas of Earth's atmosphere. However, it does play an inarguably vital role: most of the many millions of space objects (usually meteors and meteorites) which enter Earth's atmosphere burn up in this layer of the atmosphere, safely above the surface.