Entropy is defined by the way that a system's entropy changes when heat is added to it at temperature T:
dS = dQ/T
(Definitions of temperature and internal energy are developed in the same way.) dQ is not a state variable, but S is. S is characteristic of the system in the same way that P,V, T, n, and U are.
The popular statistical interpretation of entropy, that entropy measures disorder or degradation is a little off the mark. Statistically it is better to say that a system with maxmum entropy has a maximum number of choices as to which microscopic configuration it is going to take.
When the system has the maximum number of choices, it has settled into a stable state: If it changes its choice, it is likely to change into a microscopic configuration that looks the same from the outside as it did before the change. Maximizing the number of choices maximizes the stability.
If a closed system is in equilibirum, it will not change its entropy (or its other parameters, P,T,... etc.) If is not at equilibrium, it will spontaneously evolve towards higher entropy, until the entropy reaches a maximum. The other parameters, (P, T, ... etc.) follow as they must.
The most direct evidence for this is that spontaneous heat flow always proceeds from warm to cold. (It takes a heat pump to move heat the other way.) This is the direction that increases entropy. (The overall entropy of the world increases when a power company converts chemical energy to electrical energy and the heat pump uses that energy to do its job.)
When water vapor condenses into snow crystals on a starry night, the order among the water molecules increases, while the entropy of the water-air-universe system decreases. Heat is transfered from water to air, and some is radiated away into space. In the process the entropy of the water decreases. However the entropy of the universe (including the water, air, and outer space) is increased by the process.
Every bit of natural order that we observe is driven into existence by the increase of the overall entropy of the solar system.