A chemical reaction occurs spontaneously in a certain direction because that direction increases the entropy of the universe. Spontaneity is based on statistical probability. Because the new situation is much more statistically likely, the change is irreversible. How does a chemical reaction change the entropy of the universe? There are two ways it does so. The first is heat flow between the system and the surroundings and the second is change in entropy within the system. The Gibbs free energy allows us to express how chemical change affects the entropy of the universe as a function of the system.
To get a better sense of how this works, think about the equation everybody learns: dG = dH - TdS
Think about it a different way. Divide every term by (-T). This gives -dG/T = -dH/T + dS
Remember that dS = Q/T (entropy change due to heat flow equals the heat flow divided by the temperature) and restate -dG/T = -dH/T + dS in plain English. What it says is that the entropy change in the universe equals the entropy change due to heat flow plus the entropy change in the system.
What we learn in introductory chemistry is that the free energy change at equilibrium is zero. What does that mean? If we put in zero for dG in the equation we are thinking about it gives us: dH/T = dS. What this means is that at the equilibrium state the entropy change due to heat flow is exactly balanced by entropy change in the system. A little heat can flow out, but it does so without increasing the entropy of the universe, so it is just as likely to flow back. The equilibrium state is the state of the system where heat flows are reversible.
The statement above can be a very good way of thinking about if you are clear on a few things. "The Gibbs energy is a sort of potential energy - it's the energy that's stored up in the chemical bonds and in "entropy," so it's sort of like potential energy." Changes in the arrangement of particles within a chemical system leads to changes in electrostatic potential energy. In transitioning from oxygen gas and glucose to carbon dioxide and water, new covalent bonds are formed in which the powerful oxygen nucleus pulls electrons in towards itself. This electrostatic potential energy decrease corresponds to an internal energy decrease which corresponds to heat flow between the system and the surroundings (small adjustment due to pressure volume work at STP). Heat flows out. If you drop a book on a table, sound emanates into the surroundings, and it is vanishingly unlikely for the sound to coalesce and put the book back in your hands. That's why negative enthalpy change favors spontaneity. The heat flows out into the surroundings and increases entropy. Internal energy decrease (where unlike charges come together or like charges spread out) tends to produce heat flow out (depending on the pressure volume work) which tends to correspond to increasing entropy in the universe (depending on what's happening to the inherent entropy of the system.)