The wise bird
The birds are attempting to unify themselves under the authority of a truly honorable and competent leader. This can be seen as a Sufi metaphor for the soul attempting to align itself with some dominant principle. The best they can do is to turn toward the Hoopoe bird, which has often been a symbol for wisdom and power. They turn to the wise bird as a symbolic nod to the human action of repentance. By changing one's mind and deciding to pursue wisdom, an archetypal journey toward enlightenment begins. That is how to read the omens the birds are portraying in this prophetic Islamic poetry.
The mythic king
The king bird is a mythical bird, symbolizing the religious motif of salvation or deus ex machina. In order for them to successfully find their symbolic goal, they must be proven worthy by fate, and they will not know whether they are truly eligible to come into the presence of the mythic king until they have accomplished it—so treacherous is their path with trials and tribulations. One can very easily take this symbolism similarly to Plato's Republic and her magical philosopher king, or as a metaphor for meeting God.
The road of trials
The archetypal heroic road of trials and tribulations takes on a beautiful costume in this poetry. The various valleys are shown as destroyers of earthly aspects. They remove one by one what constitutes the substance of earthly interests or goals. By the end, only the birds who have more than earthly interests are shown as worthy to meet the king. The final step in the road of philosophical worthiness is to abandon attachment to money and wealth. By permanently divorcing one's self from possession, the soul is free as a bird.
The transcendental ascension
If an analysis of this poem did not mention the Sufi mysticism of it and the mythic and symbolic connections to transcendental enlightenment, the analysis would be utterly incomplete. This poetry comes from the Islamic Golden Age, at the height of one of the most important mystical movements in all of human religion. The reader must place the allegorical symbolism in that context to understand. The birds are a symbol for the soul and its journey to be united with Allah according to the gnostic principles of Sufi mysticism. This is perhaps the most similar to Buddhism that Islam can get, symbolically speaking. The mystic aspect also has a striking resemblance to Dante's Divine Comedy.
Sublime enlightenment
The imagery of sublime enlightenment is the object of transcendentalism. In this book, it is symbolized as belonging to the kingdom of the highest consciousness. So powerful is the mythic king bird that the other birds have to become heroes themselves even to tolerate the powerful presence of the ultimate being. This symbolism for enlightenment has a Western analog in the legends of Arthur's court and the Quest for the Holy Grail. In both works, the journey is to be united with the ultimate sovereignty of the universe.