Angels, Archangels, and Principalities: concern themselves with the minute ordering of the universe and specific causes, including the welfare of people. Each human being, each church, and each country has a Guardian Angel. The Feast of the Guardian Angels is October 2.
The 2nd triad:
Powers, Virtues and Dominations: known as the "angels of creation" because they concern themselves with the ordering of the universe and a plurality of causes.
The 3rd triad:
Thrones, Cherubim, and Seraphim: concern themselves with contemplating the glory of God. It is the 6-winged Seraphim who sing the Sanctus, "Holy, Holy, Holy Lord God of Hosts" (Isaias 6:3).
Angels (the word means "Messengers") are spirits (there was and is debate as to whether they are pure spirit like God or whether they are possess "subtle matter" and are corporeal in a different way from us), created before man, who were given one choice at the beginning of Creation: the Kingdom of God -- or the Absence of God, which is the Kingdom of Satan, the first Angel who rebelled.
There are 7 Archangels (Tobias 12:15). We know the names of 3 of them from Scripture:
Michael (Daniel, Epistle of St. Jude, Apocalypse of St. John), whose name means "Who is like God" and whose Feast is September 29
Gabriel (Daniel and Luke), whose name means "Strength of God" and whose Feast is March 24
Raphael (Tobias), whose name means "Medicine of God" and whose Feast is October 24.
The apocryphal Book of Enoch lists the other 4 as:
The Chaplet of Saint Michael the Archangel (full YouTube version) with Mother Angelica