This is one of many widespread terms which should be addressed when speaking of Ancient Egyptian religion. And we shouldn't try and evade it by saying that we shall never know how certain Neteru came to be associated with certain animals. We must admit -- and the Greek, Roman, and early Christian writers too were struck by the fact - That animals play an altogether unusual role in Egyptian Religion. There are too many Neteru showing such associations to not even touch on this; its most baffling, most persistent, and to us moderns, most alien feature, on this site.
It is absolutely bogus to say that the worship of animals is due to some primitive strain in Egyptian religion. Although there is some plausible debates to support this theory. Some say that these cults are of purely local significance; that sometimes center on odd little creatures like the centipede or toad, and that we must therefore place the sacred animals on par with certain sacred objects, like the crossed arrows of the Neteret Nit, and consider all these symbols as mere emblems of tribes. Some scholars even interpret them as totems, but no ancient Egyptian sources show themselves to prove this theory. Moreover, any treatment of the sacred animals which stresses their local or political significance at the expense of their religious importance is just plain silly.
it is undeniable that there is something altogether special about the meaning which animals possessed for our spiritual ancestors. It seems to me that the terror of animal strength, or the strong bond the mutual dependence of man and beast (in the case of cattle cults, for instance) explains animal worship. But in Egypt the animal as such, irrespective of its specific nature, seems to possess religious significance, and the significance is so great that even the speculation of later times rarely dispensed with animal forms when referring to the Neteru.
This much is clear, there was nothing metaphoric in the connection between Neteru and animals. It is not as if certain divine qualities were made articulate by the creature. We can clearly see the link between the Neter and actual beast, so that at times the Neteru and the animals are one in the same.
There have been findings of mummified cats, dogs, falcons, bulls, crocodiles, and so forth, buried by the hundreds in vast cemeteries which can fill anyone with the sense of severe polytheism with a vengeance!
To understand this, we should first see that the relation between a Neter and His/Her animal may vary greatly. Except in the case of Heru, who has been depicted as a falcon, or falcon-headed since the first time. Djehuty manifests in the moon, but also as a baboon, and in the Ibis, we do not know if any relation existed between these symbols at all.
The relations between the Mnevis bull and the Sun-Neter Ra, and between the Apis bull and the Creator-Neter Ptah, was different again. Ptah was never depicted as a bull, or believed to be incarnate in a bull; but the Apis bull was called "The living Apis, the herald of Ptah, who carries the truth upwards to Him of the Lovely face."
Other Neteru are regularly imagined in animal shapes but even in their case the incarnation did not limit -- it not define -- their Powers. Anpu, for instance, was commonly shown as a jackal or jackal-headed, he was by no means a Deified animal in respect to evidence.
Such "hybrid" forms are common in Egyptian art and the usual evolutionary theory explaining them as "transitional forms" intermediate between the "crude" cult of animals and the anthropomorphic Neteru of a more enlightened age. Which is utter crap, as this theory ignores the fact that the earliest Divine statues which have been preserved represent the Neter Min in human shape! On the other hand, we find to the very end of Egypt's independence that Neteru are believed to be manifest in animals.
The Neteret Hwt-Hrw appears, for instance, in late papyri and even royal statues as a cow. Yet, She is rendered already in the first Dynasty, on the palette of Narmer, with a human face, cow's horns, and cow's ears.
In any case, the Neteru are not confined to a single mode of manifestation. There is no need for a transition in manifestations, and to explain why would be pointless. The Neteru appear as He/She desires, in one of His/Hers known forms.
Our quick survey of the various relationships between Neteru and animals does not clarify the role of the latter. But the very absence of a general role and the variety of the creatures involved suggests, it seems to me, that what in these relationships became articulate was an underlying religious awe felt before all animal life.
We assume, then, that the Egyptians interpreted the non-human as superhuman, in particular when they saw it in animals -- in their inarticulate wisdom, their certainty, their unhesitating achievements, and above all, in their static reality.