Talk about functions is an import of certain metaphysical doctrines peculiar to Aristotle. He sees the furniture of the world as being composed of substances, each of which has an essence. This essence contains the properties that make the substance unique from other substances. In effect, essence is what separate cats from children. In our empirical experience, we encounter a large variety of different cats: some have no fur, some are spotted, some have no tail, some are brown, some like to swim, etc. These various properties listed that are nonessential are called accidental properties. That is, we can conceive of the cat as being orange instead of brown, and it would still remain a cat. All of this terminology has recently been resurrected by Kripke and Putnam in terms of possible worlds analysis, although their new synthesis is a somewhat bastardized version of Aristotle. For Aristotle, you cannot possible run a substance through possible world analysis and removing properties, in order to find essential properties. You must first being the inquiry with the essential properties already abstracted from the substance, else you would have no knowledge of what can go and what must stay, i.e. accidental versus essential.
While this is a seemingly abstract analysis, it is an important one. Like Plato, Aristotle bases all of his positions on certain metaphysical doctrines. His ethics, politics, physics, and biology, can only be understood with reference to metaphysics. Now within essence are four causes: efficient, material, form, and final. This excerpt from the Nichomachean Ethics is meant to illustrate the operation of the final cause, using a hypothetical imperative. If X wants to be a good X (good in terms of functioning properly of excellence), then there are certain steps that must be taken in order to achieve this end. Here the acorn and oak tree is not particularly useful, because unlike an inanimate object that just ‘tends’ on its own to fulfill its final cause. Man is a different sort of an animal. He is, in fact, a rational animal. Acorns do not write treatises on how to achieve the end of an oak. They do not have wills; they are not conscious agents. They are simply directed towards a given end because their essence has the potentiality for that end, and they are unable to thwart it. That would depend wholly on external circumstances, such as the appropriate amount of soil, light, water, etc. (efficient causes). As a side note, some do object to man ‘flourishing’ because it is usually given with the analogy of inorganic life. However, according to Aristotle, inanimate objects cannot achieve eudemonia. They are like the noncitizens of the city state.