Properties may be further classified in the following way:
An extensive variable is one which depends on system size. Examples include mass, volume.
While extensive variables are useful for characterizing the specific system being analyzed.
An intensive variable is one which does not depend on system size. Examples include temperature, pressure, density.
While it may not be immediately obvious, intensive variables tell us more about the system than extensive variables. In particular, the temperature and pressure are two of the most critical intensive variables.
A ratio of extensive variables will yield an intensive variable! (For example, mass/volume -- two extensive variables -- gives density, an intensive variable) This is one way to understand why intensive variables "tell you more".
Distinguish between extensive and intensive thermodynamic properties