I'm going to answer this question from the point of view of the Church Fathers, and in particular from the point of view of Gregory of Nazianzus, also known as Gregory the Theologian because of his enormous influence on Christian theology. Many of these themes were also picked up in the theology of Maximus the Confessor and, while they are not particularly well known in the West, they are a significant feature of Eastern Orthodox theology.
The passage in particular is Oration 38, known as On the Theophany. This is a little hard to find in decent translation on the internet, but this is one as part of a dissertation and this one is available on NewAdvent. A very good translation is that of Nonna Verna Harrison in Festal Orations. I'll quote from the first of these translations in my answer, however, because I'm currently 850 miles from my copy of Festal Orations.
In many ways, this is a commentary on the creation narrative of Genesis. Gregory sees creation as double:
- The intellectual or noetic creation: the creatures not of matter but of pure intellect. Gregory writes, "We must understand them either as intelligent
spirits, some kind of immaterial and bodiless fire, or as some other nature that is nearest
the beings described." (Or. 38.9) In many ways, these are the creatures we know as angels.
- The material creation: the creatures of visible, tangible matter. Gregory writes, "this is both the system and combination of heaven and earth, and the things between them, praiseworthy for the shapeliness of each, but more praiseworthy for the well-joined nature and harmony of the whole" (Or. 38.10) Whereas the creatures of the intellectual realm are like in nature to God, the creatures of the material realm are "foreign" to him.
So we have these two creations. They are good, but there is a limit:
Mind and sense perception then, having been distinguished from one another in this way,
stood within their own limits, and bore in themselves the magnificence of the creator
Word, being silent they praise the great work and are brilliant heralds. There was not yet
was not yet a blending of the two natures, nor any mixing of opposites, a sign of a greater
wisdom and generosity as regards the natures; nor was the entire richness of goodness
known (Or. 38.11)
Then, God creates a new thing out of both:
Then the Creator Word, having willed to show this forth, also crafts one life from both, I mean both invisible and visible natures, the man; and taking the body from the matter already created, and from himself he added the breath of life, “which thing Scripture knows as the noetic soul and the image of God” (Or. 38.11)
This is the human being, the union of the invisible (intellectual) creation and the visible (material) creation. The purpose of man is precisely this: to unite the two creations.
He continues to describe what this man is like:
He set upon earth a sort of second cosmos, a great in a small, another angel, a composite worshiper, a beholder of the visible creation, an initiate into the intelligible, king of things on earth, subject to what is above, earthly and heavenly, transitory and immortal, visible and intelligible, a mean between greatness and lowliness, the same spirit and flesh. (Or. 38.11)
In this way, the human being is the crown of creation, uniting the whole creation in one. This anthropology has a salvific purpose as well: Oration 38 goes on to discuss Christ in his Incarnation as uniting human nature to God, and therefore as uniting all of creation to God, since all creation is united in the human being.
So in this way the human is the crowning of creation. Man is "lower than the angels", according to Gregory's account, because the angels are part of first creation, in nature closest to God.