Entropy is all the fault of the second law of thermodynamics – essentially, all processes (chemical reactions included) will be spontaneous or feasible when there is an increase the entropy.
But what is entropy?
Entropy is a thermodynamic property like temperature, pressure or volume and it is best thought of as a measure of how random or disordered the molecules, and their energy, are.
If we take an ice cube and let it melt, the entropy of our system (the water molecules) increases because there are more ways of arranging molecules in a liquid than in a solid lattice. And liquid water molecules have more energy, so there is more energy to distribute amongst our more random molecules.
Similarly, if we thermally decompose solid calcium carbonate to form calcium oxide and carbon dioxide, there is an increase in the entropy because we have moved from one reactant particle to two products particles, and one of the products is a gas. In fact the reason this reaction is possible at a high enough temperature, despite it being highly endothermic, is because of the positive entropy change.
The very best introduction to the concept of entropy is to watch Brian Cox and his sandcastle.

An introduction to entropy
Entropy (S) is the true driving force of all spontaneous processes, chemical reactions included.
We can think of it as a property of matter, just like density, since its the quantity associated with the randomness or disorder of molecules and energy in a system …

How to determine the temperature at which a reaction is feasible
A spontaneous or feasible process must be accompanied by a positive change in total entropy (entropy of the universe). Whether this is the case is almost always down to the temperature – hence ice melts at 23°C but not at -14°C.

What is Gibbs free energy?
The change in Gibbs free energy, ΔG, is a convenient way to determine whether a reaction is spontaneous or feasible without having to consider the entropy change of the surroundings, ΔSsurr.
This means that ΔG can be calculated from the properties of the system (which is, of course, our reaction).