How does the atmosphere change at different latitudes?
The overall structure of the atmosphere is fairly independent of latitude. Temperatures do decrease in a poleward direction from the tropics.
The structure of the atmosphere has distinct change with altitude (see pic). Temperature changes along distinct boundaries, the pressure of the atmosphere gets less as you go up and oxygen content gets less as you go up.
As you move from the tropics to the poles, the atmosphere in general gets cooler.
The atmosphere also has some very large circulation cells that are dependent on latitude (see pic 2) and determine large scale biomes on the Earth.
The composition doesn't change but the atmospheric pressure does.
Atmospheric pressure is dependent on two things, water content and temperature. As temperature goes up pressure goes up. Therefore as your latitude increases the pressure drops.
This drop in pressure also results in a drop in the heights of the different levels of the atmosphere. For example, the tropopause (the layer between the troposphere and stratosphere) is about twice as high at the equator than it is at the poles.