An order of superiority or government among the angels, who are preeminently celestial beings.
If we consider this order from the part of God, there is but one celestial hierarchy: the absolute, supreme dominion of God over all the angels.
If, however, we consider this order from the part of the angels themselves, we find three distinct grades of superiority in which the inferior differ in perfection from the higher angels and, accordingly, are subject to them.
Each of these grades or orders is called a celestial hierarchy; "celestial" in opposition to the ecclesiastical hierarchy, i.e. the order of government in God's church upon earth.
And even as in the ecclesiastical hierarchy, there are three grades, bishops, priests, and deacons, subordinate one to the other; so, too, in each angelic hierarchy there are three groups differing in perfection and power, one from the other.
These subdivisions of the angels are called choirs.
New Catholic Dictionary