Aristotle gives five meanings of before and after:
1. Before in time. 2:00 PM is before 3:00 PM.
2. Before by nature. The existence of man implies the existence of animal, but the existence of animal does not imply the existence of man, so animal comes first.
3. Before in understanding. The premises of an argument come before the conclusion.
4. Before in goodness. The better thing is first.
5. Before in causality. The cause is before the effect.
The world is ordered in all of these ways, and the various orders have certain relationships. The order of time lines up with the order of nature to some extent, since if a thing implies the existence of something else, it cannot exist temporally before the thing the existence of which it implies. Thus animals existed before human beings, but not human beings before animals. This order is never reversed, but sometimes the order of nature does not also include an order of time. Thus the first bodies must also have been some particular kind of body; there was no temporal sequence there.
For material, formal, and efficient causes, the cause is always simultaneous in time with the effect. However, on account of its causal priority, that which constitutes the cause sometimes comes temporally before that which constitutes the effect, and never the other way around. Thus in this sense the order of the things which are causes to some extent shares in the temporal order in the same way that the order of nature does.
The final cause is sometimes taken as that which is loved, and in this sense it has no definite temporal relation to its effect. Thus sometimes it comes after, as the money which is loved makes a man work for it, and sometimes it comes before, as the wife who is loved makes a man praise her even after her death.
But when the final cause is taken as that which is desired but not yet possessed, it always comes after its effect, assuming that it comes to be at all. This results in a temporal order which is reversed according to final causality, but which corresponds to the order of goodness. What possesses the good is better than what does not possess it, and comes after in time, unless something fails such that the efficient cause which sought the final cause does not succeed in attaining the good it desired.
Thus a successful world is one in which the order of time basically corresponds with the order of causality and the order of goodness. This is what St. Thomas means when he says that the good of the world consists in its order, and that its order consists principally in the fact that one thing is the cause of another, and that one thing is better than another.