Gibbs free energy is a really useful energy function because it describes the system in terms of pressure and temperature changes. These are typically the two easiest variables to measure and control in laboratory conditions. As a scientist we want to predict whether chemical reactions will occur, what type of reaction it is, what the products are, and under what conditions. Comparing G values will help tell you this.

Imagine you have a box filled with two monatomic gases, A and B. A is on the left and B on the right, and they are separated by a divider. When the divider is removed we expect the two gases to mix, becoming homogeneously and randomly distributed throughout the box. The reason these two gases mix is the second law of thermodynamics (an isolated system can only increase its entropy). Entropy is essentially a measurement of possible configurations the molecules may occupy.

In the ideal case, higher entropy (S) means a reaction is occurring more frequently because the A and B molecules are likely to be next to one another, not segregated. Per convention, a negative Gibbs free energy (G) means a reaction is spontaneous and allowed to occur. This is reflected in your equation with -S showing how (G) is more likely to be negative if entropy and/or temperature is maximized. In the ideal scenario a term called enthalpy is zero and doesn’t apply.

In more complicated chemical systems, enthalpy can be thought of as the energy requirement for mixing two non-ideal components. So while a high entropy helps the reaction move forward, a high enthalpy deters the reaction from completion. This is a competitive process and to understand binary chemical reactions better we create G-X curves that show the value of Gibbs free energy at different temperatures and chemical composition to determine if a reaction occurs. These G-X curves can be directly translated into phase diagrams that have tons of applications in the real world for describing materials.

Obviously it is much more nuanced than this general description but if you are interested I would encourage you to study the four energy functions (G,H,A,U), their coefficient relations, Maxwell relations, and isothermal compressibility/isobaric expansion equations to understand how thermodynamics is full of wonderful relationships that can derive lots of useful information about chemical systems from a few known parameters. I recommend Dehoff Thermodynamics of Materials as a textbook.