In the breeding, we take two members of a population and generate one or more child, where that child represents a combination of its parents.
In our NN(neural network) case, each child is a combination of a random assortment of parameters from its parents. For instance, one child might have the same number of layers as its mother and the rest of its parameters from its father. A second child of the same parents may have the opposite. You can observe how this mirrors real-world biology and how it can lead to an optimized network quickly.
Polyworld is a framework for Artificial Life (ALife). With ALife, the survival of individual creatures and their ability to pass their genes to other generations. It is tied to various broader, non-goal-oriented, criteria, such as the ability of the individual to feed itself in ways commensurate with its size and its metabolism, its ability to avoid predators, its ability to find mating partners and also various doses of luck and randomness.
Polyworld's model associated with the creatures and their world is relatively fixed (for example they all have access to (though may elect not to use) various basic sensors (for color, for shape...) and various actuators ("devices" to eat, to mate, to turn, to move...) and these basic sensorial and motor functions do not evolve (as it may in nature, for example when creatures find ways to become sensitive to heat or to sounds and/or find ways of moving that are different from the original motion primitives, etc...)