Why did the apple fall from the tree, vis-à-vis the second law of thermodynamics?

If you want to know how falling of an apple increases entropy, you can think about it like this: When an Apple falls, it interacts with the earth through the gravitational fields and thus force carriers are continuously exchanged between them. The re-arrangement of the net energy of system and force carriers makes it chaotic, thus entropy increases.

The same theory applies to electromagnetic forces of attraction and repulsion.

To add to BySymmetry's answer, I would like to provide a quote from Eddington's "The Nature of the Physical World"$^*$, in which he discusses the link between the second law of thermodynamics and our perception of "time's arrow".

There is only one law of Nature⎯the second law of thermodynamics⎯which recognizes a distinction between past and future more profound than the difference between plus and minus. It stands aloof from all the rest. But this law has no application to the behavior of a single individual.

In your case, the "single individual" is the apple moving in the presence of the gravitational field.

One must remember that entropy, temperature, etc. are concepts from statistical mechanics; which we apply to ensembles of many, many constituents because to track each part individually would be utterly impossible. Therefore, it is not very meaningful to apply the ideas of "entropy" or "temperature" to a system of one or even two bodies. As Eddington also says in the above reference:

it must be remembered that many properties of a body, e.g. temperature cannot be regarded as controlling the behavior of a single individual.

So, I might go one step further from BySymmetry's answer and say that Gibbs would have found the question to be somewhat meaningless.

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$^*$This is a great text to read that, while over 90 years old, gives an accessible overview of many areas in physics and specifically gives good intuition behind entropy. It also has one of my favorite quotes:

The law that entropy always increases⎯the second law of thermodynamics⎯holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations⎯then so much the worse for Maxwell’s equations. If it is found to be contradicted by observations⎯well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.

The question that the second law of thermodynamics really addresses is not "why does the apple fall from the tree" but instead "why, having fallen from the tree, does the apple not leap back into the tree again ?". When you throw a stone into a pond it causes ripples which expand outwards. That is not mysterious. What is mysterious is that we never see ripples which converge on the stone and then project it back to your hand. That is what the second law of thermodynamics answers.