A thermodynamic process moves a system from one thermodynamic state to another.
Why should we care about thermodynamic processes?
Answer: What happens inside any engine? Thermodynamic processes! compression, expansion, heating, combustion, etc.
Generally we consider quasi-static processes, where the state changes so slowly that we can regard the gas as always being in equilibrium.
It is useful to follow ideal-gas processes in the PV diagram. Using the ideal gas law PV=nRT, the
temperature is known for any P and V, from which the state of a gas is
uniquely determined.