Although discussion of the detailed application of the phrase involves opinion, there is a general meaning that is not dependent on opinion. I therefore do not vote to close, but instead attempt an answer.
One of the early examples of the use of the phrase is by William Paley:
Google
The fitness of things, means their fitness to produce happiness: the nature of things, means that actual constitution of the world, by which some things, as such and such actions, for example, produce happiness …
When we look for contemporary meaning, we find
Collins
Fitness:
1 the state of being fit
2 biology
a. the degree of adaptation of an organism to its environment, determined by its genetic constitution
b. the ability of an organism to produce viable offspring capable of surviving to the next generation
And
Cambridge
Fitness:
the quality of being suitable for someone or something
Without producing more tedious examples, it is clear that the term generally relates to some sense of order or purpose. The role of the world or the part of it in question is arranged such that it is ordered rather than chaotic or unpredictable, and such that some purpose is served, such as the pursuit of happiness, or the continuation and reproduction of things.