When most people think of "atmosphere" they think of a single envelope of gases surrounding the Earth. What's very interesting, however, is that this "envelope" isn't just a uniform region of gas. It's actually divided up into several different layers. Now, it's important to note that the boundaries between these layers aren't hard lines like the layers in a cake, they blend together.
The atmosphere becomes more transparent as it gets thinner. Source
The first layer, closest to the surface of Earth, is known as the troposphere. It extends about 17 km from the ground on average, but can extend higher closer to the equator, or lower around the poles. This region contains about 80 percent of the atmosphere's mass and 99 percent of its water vapor.
After the troposphere is the stratosphere, but in between is the tropopause. The tropopause is the boundary between the troposphere and the stratosphere. It is a region of nearly uniform temperature and complete dryness. It also marks a change of a different, and more interesting, kind. If anybody has ever climbed a mountain, they're sure to have noticed that the air becomes colder the higher they get. This is an aspect of the troposphere that seems intuitive. However, temperatures don't behave this way in the stratosphere. Instead of cooling as the altitude increases, the stratosphere actually warms up. This is because it contains most of the atmosphere's ozone (O3) which absorbs ultraviolet radiation from the sun, converting it to heat. This layer can begin at as low as 10 km and go to around 50 km. These boundaries, like all atmospheric layers, are subject to change with season, storms and other effects, however.
Atmospheric boundaries. Source
Another look at atmospheric boundaries. Source
Next we have the mesosphere. By this point the air is really thin and the temperature is really low. However, the mesosphere goes back to the more intuitive "cooling with increased height" temperature scheme. There's not much to say about the mesosphere. It begins at around 50 km and ends somewhere around 100 km, but again, this is subject to change depending on the season.
Above the mesosphere and before the next layer is another boundary layer. This boundary, known as the mesopause, is unique because it can reach the coldest temperatures found naturally anywhere on Earth. It can get as low as 130 K, that's -143 C or -225 F. That's really, really cold.
The next layer is the thermosphere. This layer is unique in that it is not chemically mixed. Every layer previous was a more-or-less uniform mixture of various gases, but the thermosphere is so sparse and cold that it doesn't mix well. This layer of the atmosphere is separated out by the weight of the molecules that form it, with the heaviest molecules on bottom and the lightest on top. This layer is also similar to the stratosphere in that its temperature increases as altitude increases. This happens because the particles here absorb high energy solar radiation.
The thermosphere is the outermost layer of the atmosphere we all think of. Source
There is one final layer to the atmosphere. In any normal conversation about the atmosphere, most people would stop at the thermosphere, seeing as how it's the outer layer of any atmosphere that we would be able to feel, but I'm not going to stop there. The final layer is known as the exosphere. Here the "air" is so thin that particle collisions are very rare. This portion of the atmosphere mixes with space, so it has no defined ending point. One peculiar consequence of this, however, is that gas can leak out into space from here. This is known as the "slow leak" phenomenon. Most of us think of Earth's atmosphere as a solid shell around the planet, but it is actually leaking away. The loss of gas particles is incredibly slow, but given enough time (a very, very long time) our atmosphere could float away entirely. Now isn't that a scary thought.