State of a function (system) is a condition of existence which is described by some measurable properties. For e.g.: water exists in three different states i.e. solid, liquid & gas depending upon the temperature at 1atm pressure.
The measurable properties of gaseous system are pressure, temperature, volume, mass or composition of substances. Any change in these properties will change the state of a system and these properties are called state variables.
Some state variables depend only on the initial and final state but not the path or process how it is carried out, and they are called state function.
If water is heated from 0°C to 50°C, then we say that the change in temperature is 50°C regardless the process how water is heated.
Also, the vol. of 1 mole of any gas at NTP condition is 22.4 L regardless the process how that gas is prepared.
Depending upon the properties, there are two types of state variables:
Those state variables that depend upon the quality of matter are called extensive variables. For e.g.: mass, moles, volume, internal energy, enthalpy, entropy and free energy.
Those state variables that depend upon the property of matter are called intensive variables. For e.g.: temperature, density, refractive index, etc.