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To have a complete understanding of entropy pretty much requires a degree in Physics (which I possess), but can be broken down easily enough without the math. One must begin with the Second Law of Thermodynamics which states that the total entropy of any isolated thermodynamic system tends to increase over time, approaching a maximum value. In other words, differences in systems that are in contact with one another tend to even out over time (think of a hot pan cooling after taken from its heat source). Energy of some kind is changing from being localized ("concentrated" in the pan) to becoming more spread out.

Entropy measures the spontaneous dispersal of energy: how much energy is spread out in a process, or how widely spread out it becomes — at a specific temperature. Simply put: how much energy is dispersed is a measure of entropy. The energy is "out there", but no longer a part of the system. It actually becomes part of the surroundings (or universe). From the First Law of Thermodynamics (conservation of energy) we know that this energy has to go somewhere.

So what the aych-ee-double-toothpicks does this have to do with evolution? Energetically, the second law of thermodynamics favors the formation of the majority of all known complex and ordered chemical compounds directly from their simpler elements. Thus, contrary to popular opinion, the second law does not dictate the decrease of ordered structure by its predictions. It only demands a "spreading out" of energy when such ordered compounds are formed spontaneously. The Second Law does NOT prohibit the spontaneous formation of complex structures from simpler parts. It is simply incorrect to view the Second Law as a predictor of disorder.