Understanding Entropy

Hi, Benjamin here. The day has finally come that I slightly understand what entropy is-- I think so, at least. Through highschool, entropy was labeled as the level of disorder in a system, and as entropy always increases, there's a pretty glum lookout, especially for people who like to be organized.

In Chemistry class yesterday, we went a bit further into what entropy was. The new, but admittedly  still inaccurate definition the professor gave us was this-- entropy measures the amount of possible configurations of a system. I will now test my understanding of this new concept by trying to explain it:

Imagine two crates of eggs, a dozen egg-holes in each. One crate is full of eggs and the other has none. In this situation, entropy is very low-- there's only one possible arrangement of eggs in the full crate (every hole full) and one possible arrangement in the second (every hole empty). This first arrangement is also very 'organized', though it can be hard to define that. If, however, one egg was moved from the first crate to the second crate, there would be 144 possible arrangements, if my calculations are right. In the first crate, the empty hole could be any of the twelve, and in the second crate, the full hole could be any of the twelve. There are more possibilities, so entropy has increased.

If you go ahead and decide to put each of the twelve eggs in any of the twenty-four holes, there's a huge number of possible arrangements, and thus a large amount of entropy, and, most likely, disorder as well. What's the real difference then? Why not keep using disorder as a definition for entropy?

I guess it takes another example to show the difference. When oil and water are mixed together, they separate because of entropy, forming, in a way, a more 'ordered' arrangement. This doesn't make sense from a pure 'entropy as disorder' point of view, but when thinking of possible arrangements, I think it makes a little bit more sense. If a water molecule is theoretically surrounded by ten water molecules and ten oil molecules, it has ten molecules it can interact with and bond with (like interacts with like). When the same molecule is surrounded by twenty water molecules, it has twenty 'choices'. More entropy, but entropy that results in a clearly defined separation between oil and water.

This is a small step in my understanding of entropy, and still very tentative. It turns out that entropy is measured in joules, and I have no idea why that is yet. I'd like to know if anyone reading this actually does understand entropy and could explain it a bit further. Moreover, I'm wondering who else is out there who, like me, never really understood entropy in the first place.