What is the phase rule and what does it indicate?

Gibbs' phase rule is the fundamental rule on which phase diagrams are based. It gives the number of degrees of freedom for a given thermodynamic condition, that is: how many control variables (pressure, composition, temperature, etc) can be changed whereas maintaining this condition. Mathematically, this number is

   P + F = C + 2 

Where P denotes the number of phases in equilibrium coexistence (solid, liquid, gas phases etc) and  C denotes the number of chemical components in the system.