I was not very impressed by angels until I was on a 30 day retreat in September many years ago and was enlightened about what angels really are while at Mass one day. During my retreat I attended Mass every day at a lovely parish in Swissvale, PA, (a section of Pittsburgh). There was a visiting priest who said Mass on the Feast of the Archangels and he changed both my perception and appreciation for my patron forever. He said, "Since angels are neither male nor female for all we know St. Michael was actually St. Michele." I was immediately sold! I know that is not a good reason for being attracted to a patron, and I do realize he was being a bit flippant while in fact teaching a truth about the angels who do not have a gender. But it did catch my attention. It began a new-found understanding and appreciation of what angels actually are and what they do for us.
Unfortunately the New Age movement and all sorts of other secular trends have trivialized angels. We see them everywhere it seems: gift stores, card stores, book stores, misrepresented in movies, and the like. These secular and quasi-religious trends have given many of us the wrong idea about angels. They are not cute and cuddly like naked babies with wings, and they are not something bordering on science fictional or superstitious. They are not people who died and were so good that they were given wings, such as we see in the movies. (Those are saints, by the way.)
Angels are spiritual beings who have free will and intelligence. They have no gender since they do not need to procreate. They are pure spirit; that is, they have no corporeal bodies as we do. The word angel means "messenger" in Hebrew and that is one of their roles. They are God's messengers. Throughout the Old Testament there are numerous instances of angels acting as such. Most of the time when God seems to be speaking in the Old Testament it was really one of His angels who delivered the message for Him. They are described in many instances and we know that Jewish tradition (in addition to the Old Testament) teaches that there are many types of angels, all of whom were created at the beginning of time. They were given the same gift of free will as humans eventually received. The tradition teaches that when one high ranking angel, Lucifer, (the angel of Light) rebelled, refusing to serve any longer, some angels took up with him and rejected God. These left Heaven as fallen angels and their leader is referred to as Satan, which comes from a Hebrew word which means "an adversary; one who opposes God." The angels made their choice and it is sealed for eternity. Therefore the angels who serve God, while still maintaining their free will, are close to God and therefore will ever remain faithful.
The tradition teaches us that there are nine choirs of angels. In order, they are Seraphim, Cherubim, Thrones, Dominions, Virtues, Powers, Principalities, Archangels, and Angels. (See http://www.catholic.org/saints/angels/angelchoir.php for information and a description of each type of angel.) In the Scriptures the three named archangels celebrated on this feast day are Michael, Gabriel, and Raphael. Michael means "who is like God?" and it refers to his single minded service of God whom he glorifies through his service at the head of the Heavenly Host of Angels. He is the protector of God's people. Gabriel is the messenger who delivers important messages and who announced the coming of St. John the Baptist to Zechariah and the Son of God to Mary, His mother. The third archangel is Raphael who brings healing, and is described in the book of Tobit for helping Tobit and a woman named Sarah, both of whom needed serious healing.
I think it is important to note that the New Testament also tells us of angels, both good and bad. Jesus was ministered by angels after He was tempted in the desert and also He was comforted by an angel in the Garden of Gethsemane. (He also cast out demons, so we know that He attested to those types of angels as well.) Angels are important to us because they protect us and come to our aid when we need their help. They are compassionate and loving, serving our God who is Love. The Catechism tells us that each person has a guardian angel. Therefore it is important to ask for their protection when we think we may especially need it, and it is important to say thank you when we have come to the conclusion of whatever situation safely.
Often when someone has done an especially good or heroic deed people will say "what an angel" or something like that. We can indeed imitate the angels by being thoughtful towards the needs of others, by serving quietly and humbly, and by being "other-centered." Maybe the Holy Spirit is motivating us and an angel is carrying that message to us, so we can act like an angel. Either way, angels are all around us, protecting us and attempting to give us the message that we are very loved by God. While angels are important, we are still the most important beings God has created; He has given us angels to try to help us to be protected and aided in times of trouble.
Let us call upon the angels and archangels when we are in need of guidance or protection. Let us be especially grateful for the power of St. Michael the Archangel who is the one who leads the Heavenly hosts against the powers of evil. Let us be mindful of the messages delivered by St. Gabriel that brought about our salvation, and of the healing power of St. Raphael who delivers God's healing touch to us. Finally, let us give thanks to God for the wonders of the spiritual world He created which help us to stay with Him and return to Him at the end of our lives. Let us meet in the Heart of our Lord, along with the angels and saints. Peace!
(By the way, a note about what seems to be a contradiction in what I have written about angels and in my comment about saints above: Angels are not really saints according to definition. A saint is a holy person who is now in Heaven with God. Angels were never human. But we traditionally call Michael the Archangel, for example, St. Michael as a sign of honor for his closeness to God and his role in salvation history and the same for the other two archangels mentioned. This is not true of any other angels.)
Some other sources about angels are the Summa Theologica of St. Thomas Aquinas and The Catechism of the Catholic Church . A book I find very helpful is Angels (And Demons) by Peter Kreeft. It is in question and answer format, but he synthesizes much of the wisdom of Aquinas and other spiritual masters into his writing.