What separates the layers of the atmosphere?
Layers that we call "pauses" and they generally are determined by temperature contrast.
To explain this best I will just look at the first pause, the tropopause. The tropopause is at the top of the troposphere and separates it from the stratosphere. As air rises through the troposphere it cools due to reduced air pressure (Gay-Lussac's law). In the tropopause the lapse rate (rate that the temperature changes with height) goes from cooling with height (as in the troposphere) to a neutral lapse rate (basically no change with altitude) to eventually warming with altitude, which is what we see in the stratosphere.
Incidentally, the reason we see the warming in the stratosphere is because this is the point of the atmosphere where the ozone layer is. The absorption of UV light by ozone.