There is a speculative, general scheme of the evolution of the concept of God that is criticized because it cannot be proven in detail and because it (sometimes or necessarily?) manifests complacency and pride, as though the theorist's own religion (in its present state) were the standard by which to measure the progress of everything else. The implication that some religion is "primitive" is unwelcome to most scholars of religion today. Nevertheless, the picture is worth considering as a point of departure.
The first stage of religion is ghost fear. The shock of death and dreams of departed ancestors give rise to the idea that the ghosts of the dead remain in the community to guard jealously the traditional customs and to bring bad luck upon those who violate them. Belief in the spirit world motivates the first ethical discipline. Animism is a stage in which spirits are regarded as indwelling special or unusual natural things. Then the idea of gods evolves, beings of greater power, immortal, controlling one force of nature or another, or supervising some aspect of daily life. Then comes the stage of henotheism (from hen, Greek for "one," and theos, Greek for "God"), in which one of the gods is regarded as supreme over the others. Then comes the stage of monotheism (from mono, Latin for "one") in which it is affirmed that God is one, and there are no other gods beside him. Then, on some accounts, comes the conception of a trinity--Deity unity articulated as three divine personalities, or ultimate Reality manifest in a three-fold way (Brahma, Vishnu, and Shiva in Hinduism; the Buddha, the Dharma [teaching], and the Sangha [religious community] in Buddhism; the Father, the Son, and the Spirit in Christianity. And there are still more complex theologies. According to Judaism and Islam, however, trinitarian theologies betray the unity of God.
Why, according to an evolution of religion theorist, does the concept of God evolve?
One idea is that reflective thinking causes religion to progress, despite the weight of conservatism in the transmission of tradition. The mind that wants to synthesize and integrate a unified and harmonious understanding of the cosmos and divinity may not be satisfied to with a polytheistic universe run by a committee, or with the tension implicit in going to one god for this concern and to another god for another concern. When concerns overlap or conflict, what do you do?
Next, there is the process of "deanthropomorphizing." If evolutionary religion creates anthropomorphic gods (from anthropos, Greek for "human being," and morphe, Greek for "form")--God in the image of man--philosophic reflection moves to take away the merely human aspects of the concept of God--the petty jealousy, the rage, the adulteries and deceit. (Note that this process can end up by totally depersonalizing the concept of God altogether, as in Brahmanism.) The move beyond a simple monotheism may be motivated by the difficulty of conceiving and relating to an abstract, removed Deity that has no relationships to other and equal personalities.
Finally, religionists who affirm evolution may conceive that the Creator designs the basics, and governs the eventual outworking, of the process of evolution, punctuated at times by revelation.