They allow to simplify calculations/measurements related to real processes, as they take into account the effect of the environment.
Take for instance enthalpy, ##H \equiv U + PV## or its change at constant pressure ##\Delta H = \Delta U + P \Delta V##. Imagine you have a process that will lead to an increase in the internal energy (##\Delta U > 0##) and expands (say a gas phase reaction where two molecules of reactant give 3 molecules of products). ##\Delta H## tells you the energy needed for the process by considering not only the increase in internal energy but also the work that has to be done against the environment.
Likewise, for instance, the Gibss free energy takes into account both the exchange of volume and of heat with the environment. For a chemical reaction ##A \rightleftharpoons B##, in an open container, the values of ##\Delta G## tell you immediately which way the reaction will go by itself. Simply knowing the internal energy ##U## is not sufficient.
Another example: why is water liquid at 99°C, and not a gas? Surely the gas has more entropy than a liquid, and therefore should be favored? Check the Gibbs free energy: it is lower for liquid water at 99°C than steam at the same temperature.