These are God's (or more specifically Jesus') created spiritual beings (Hebrews 1:14) that do His will. They were created before us humans (Job 38:4-7) at a level a little higher than us humans (Hebrews 2:5-8). In relation to us humans God uses them primarily as messengers and teachers (Hebrews 1:14 "Are not all angels ministering spirits sent to serve those who will inherit salvation?"), but has also used them for other tasks such as guarding the Garden of Eden (Genesis 3:24), the Angel of Death to kill the first born (Exodus 12:12), weeding out the saved from the unsaved at the end of the age (Matthew 13:41), etc....
God's Word, for the most part, doesn't categorize the Angels except in specific cases:
First, we have the Archangels Michael and Gabriel. Michael has the special task of caring for Israel, and Gabriel communicates special messages to God's servants.
There is also, in the Old Testament, the "Angel of the LORD". This Angel is depicted as a visible manifestation of God Himself, or Theophany. He has powers and characteristics that belong only to God, such as the power to forgive sins (Exodus 23:20-21 "... he will not forgive your rebellion, since my Name is in him.").
Cherubim, Seraphim and living creatures (or living beings) are usually the Angels found in God's presence, guarding the Garden of Eden, or portrayed on the Ark of the Covenant and in God's Holy Temple. Note that at one time, prior to his rebellion, Lucifer was a Cherub.
Destroying Angels described in Psalms 78:49 "He unleashed against them his hot anger, his wrath, indignation and hostility--a band of destroying angels." Plus at the Passover in Exodus 12:23 "... he will not permit the destroyer to enter your houses and strike you down."
Finally, there is the "angel of the Abyss" as described in Revelation Revelation 9:11 whose name in Hebrew is "Abaddon" and in Greek is "Apollyon". There are 2 schools of thought regarding this particular angel. Either he is not fallen or, as some believe, he is a fallen angel. Whatever the case, obviously his duties are very unique.
As to their general appearance, there is no description other than that they are spiritual beings, yet there are specific examples:
The first one we will look at is the Cherubim guarding the Garden of Eden in Genesis 3:24 "After he drove the man out, he placed on the east side of the Garden of Eden cherubim and a flaming sword flashing back and forth to guard the way to the tree of life." Which actually doesn't describe the look, but more the power and ability.
In Genesis 19:1-5 we find that 2 Angels took on human form. They looked like men and must have been very good looking "... all the men from every part of the city of Sodom--both young and old--surrounded the house. 5 They called to Lot, "Where are the men who came to you tonight? Bring them out to us so that we can have sex with them."
Then there is the instructions regarding the design of the Cherubim at both ends of the Ark of the Covenant in Exodus 25:20 "The cherubim are to have their wings spread upward, overshadowing the cover with them. ..."
The Angel at Jesus' tomb Matthew 28:3-4 "His appearance was like lightning, and his clothes were white as snow. 4 The guards were so afraid of him that they shook and became like dead men"
The Seraphim in Isaiah 6:2 "Above him were seraphs, each with six wings: With two wings they covered their faces, with two they covered their feet, and with two they were flying."
Finally, we have a general description in Judges 13:6 "... He looked like an angel of God, very awesome."
God's Word doesn't give us a specific number, but in Psalms 68:17 "... tens of thousands and thousands of thousands..." we are impressed with the idea that there are a lot of Angels. Plus, David's account is given after 1/3 of all the Angels rebelled.
In Revelation 12:3-9 we learn that there was "... war in heaven. Michael and his angels fought against the dragon, ..." and that "His tail swept a third of the stars out of the sky and flung them to the earth. ..." For more detail [refer to "Fallen Angels"]
God's Word tells us in Hebrews 13:2 "... some people have entertained angels without knowing it." So, as a Born again Christian, we should be aware whether an entity is from God or not from God. Below is a simple 2 question test:
Did the entity or occurrence maintain Biblical soundness? Or, in other words, God's Word was not contradicted.
In 1 Corinthians 6:3 Paul is describing a future aspect of our relationship with Angels: "Do you not know that we will judge angels?..." It is thought that since us humans, unlike the Angels, were given "the sin nature" [refer to "Sin Nature"] at birth, but more importantly given the ability to freely choose to rebel against God utilizing an adversary, God holds us humans in higher esteem above the Angels. This might be the reason that Satan (Lucifer) [refer to "Satan"] and his fallen angels [refer to "Fallen Angels"] rebelled against God.
The secular world seems to be more interested in the fallen angels rather than of God's personal Angels. And when an occurrence or appearance of an entity of unknown origin occurs, only then the secular world will jump to the conclusion that it was some sort of angel. As for other religions, angels are very predominant and also perform all sorts of tasks. So, be careful when speaking to others about angels that you clarify which angels are being discussed.
We are told that Angels are God's ministering tools for those that know Him. God created a lot of Angels, how many is not revealed, and they do not pro-create. Unfortunately, through selfish pride, a third of the Angels rebelled against God and were banished from God's presence [refer to "Fallen Angels"]. So, however many thousands upon thousands of Angels exist, we know a few things about them. They are God's personal servants doing his will. Their name "angel" means messenger. Angels were present at the creation of the world [refer to "Creation"], they delight in praising God, they rejoice every time a person becomes a part of God's personal family [refer to "Salvation"], they are always available to help, guide and protect all of us Born again Christians, they meet a wide variety of human needs such as relieving human hunger and thirst, they sometimes deliver the people of God from danger, they sometimes are God's agents for destruction and judgment of evil, plus many other tasks as desired by God.
As a side note, Angels of God in the Bible usually interact only with good people.