The real differentiating factor between the birth of the Avatar and the other Beings in the manifestation is the self-awareness of knowledge that the Avatar brings with him; and the consequent ability of the Avatar to provide guidance and direction to the growth of consciousness in the manifestation towards a similar self-aware status of knowledge.
Consciousness is involved in Matter, as can be recognized when we view the precise and powerful organization of matter at the atomic level. It is however not self-conscious at that stage. As it evolves successively through the stages of plant life, animal life and human life, we see an ever-growing conscious awareness. This sets forth the pattern of the evolution of consciousness towards higher and more self-aware states that eventually leads to the level of the Divine Consciousness which is all-aware and self-aware.
The aspiration or seeking from below is met by a response from above, and in certain instances, where an evolutionary leap is required, the birth of the Avatar represents the response from above in a concrete and very specific way. Sri Aurobindo explains: “The Avatar therefore is a direct manifestation in humanity by Krishna the divine Soul of that divine condition of being to which Arjuna, the human soul, the type of a highest human being, a Vibhuti, is called upon by the Teacher to arise, and to which he can only arise by climbing out of the ignorance and limitation of his ordinary humanity. It is the manifestation from above of that which we have to develop from below; it is the descent of God into that divine birth of the human being into which we mortal creatures must climb; it is the attracting divine example given by God to man in the very type and form and perfected model of our human existence.”
Sri Aurobindo, Essays on the Gita, First Series, Chapter 15, The Possibility and Purpose of Avatarhood, pp. 147-148