The Angels were an immediate creation of God, in His Image and Likeness. The main purpose of their existence is to love and serve God in Heaven, as ours is to love and serve God on earth. In addition, God has given them a whole list of other jobs to perform. In essence, they are contemplatives in action. The work they do on behalf of the world and humanity is really an outpouring of the love that comes from being in the Beatific Vision of God. Angels are not human; they are actually superior to man. They might be our big brothers. Scripture tells us we are "a little less than the Angels".
In question 50 of his Summa Theologica, Thomas Aquinas gives us an understanding of the substance of Angels, by categorizing the different degrees of existence of all creatures. He breaks creation down into three groupings, animal, human and Angelic. Animal is completely body. Human is a mixture of body with something extra added, a spirit. Angels are pure spirit, without body at all. "Pure spirit" are the key words here. Because the Angels are pure, they are not corrupted by matter. Therefore, they can't die, or decay, or do anything else that results from being made of matter, like animals and humans. Also, they're not dependent on matter of any kind for their existence. They don't need food to eat, or air to breathe, or water to drink. They are pure.
Another exciting thing about the Angels, is that each one is a unique, one of a kind creation of God, like a snowflake. I used to have a problem with this. I didn't quite understand what I was reading. Penny explained it to me. It meant exactly the same as what we tell people about themselves when we give talks. Each of us is a unique, one of a kind creation of God. There is no person on earth that is quite like the creation you see when you look in the mirror. The same applies to the Angels.
The only difference is Angels don't have to look in mirrors. They are not burdened down with bodies. This has been a problem for humans from the earliest days, because we need to see Angels to understand them, and the only way we can see them is if they have bodies. How can we see Angels with bodies if they don't have them? It's the same as seeing God, the Father, as an old man with white hair and a long white beard, and brilliant white flowing gown. It's a picture we paint of what God might look like, if He were human, and had a body. It's really more for our benefit than it is for Him.