Thickness when discussed in relation to the atmosphere, is measured as the vertical distance between two points of equal pressure. The ability to divine useful information from thickness is rooted in the ideal gas law, which states that increasing temperature requires lower density and increased volume.
Lower level thicknesses help to understand the temperature near the surface, and is often used to forecast precipitation types. Colder air at the surface, but a higher than expected thickness can indicate sleet or freezing rain, for example.
Monitoring isopleths, or lines of constant thickness is the most effective way to establish changes in airmass, and distinguishing between surface based temperature changes and true cold or warm fronts.