State Function:
If a system is in equilibrium, the variables like its volume (V), pressure (p), temperature (T), etc have definite values. So, these values refer to the state of the system. So, the variables like volume, pressure, temperature, etc called state function.
Path Function:
On the other hand, the two functions – work (W) and heat (Q) are not related to any state of the system, rather they are relevant to any process of the system. A statement WA is the amount of work done in the state A – has no meaning. Rather the statement ‘WAB is the amount of work done in the process A -> B is meaningful.
There can be various paths from state A to state B. The values of WAB or QAB in each path are different. These values depend on the paths between the states A and B. So, W and Q called path function.