The word appears numerous times in both the Old and New Testaments, in three different languages: Hebrew, Aramaic and Greek. In all three languages the definition is "messenger." They are spiritual beings (Heb. 1:14), superior to humans with superhuman power and knowledge (2 Sam. 14:20; 2 Pet. 2:11), but they are not all-powerful or all-knowing. Artists generally portray them as winged beings, and I suspect they are, but that cannot be confirmed in the Bible, except for certain types or classes of angels that I'll describe later.
Angels were created by God (Ps. 148:5) and were present when He created the world (Job 38:4-7). They were originally all holy, but sometime in eternity past some of them rebelled against God. The leader of this rebellion was an angel named Lucifer (morning-star) (Isa. 14:12) who was cast out of Heaven and became the devil, also known as Satan, the serpent, the dragon, etc. When Rev. 12:3-4 describes an event in Heaven where a great red dragon (Satan) "drew the third part of the stars of Heaven, and did cast them to the earth," it is believed to be a reference to a third of the angels who followed Lucifer in his rebellion. Those angels are the "fallen angels" Jude 6 tells us are "reserved in everlasting chains" awaiting judgment. The rest of the angels are known for their reverence for God and their obedience to His will.
Only four angels are named in the Bible: Michael, Gabriel, Lucifer and Abaddon, also known as Apollyon. Michael is the only one called an archangel (chief angel), but Dan. 10:13 calls him "one of the chief princes," so there is at least one other, and most Bible scholars think it's Gabriel, and it's possible that Lucifer was one in the beginning. Michael is the guardian of Israel (Dan. 10:21; 12:1), the commander of the angelic army (Rev. 12:7). Gabriel, who describes himself in Lk. 1:19 as one who "stand in the presence of God," communicates special messages to God's servants, and is considered to be in charge of the angelic messenger corps. Lucifer was probably in charge of the angels whose primary function was praising God and serving as His throne attendants. He is usually described, jokingly or not, as the choir director. The fourth named angel, Abaddon (in Hebrew) or Apollyon (in Greek) is the king of the demonic beings locked in the bottomless pit of Hades (Rev. 9:11). These four names are all male names, and there is no hint in the Bible that there are any female angels. Most of them are just called angels, but on one occasion Daniel uses an Aramaic word that is translated "watchers" in the KJV (Dan. 4:17), then there are the angels called cherubim, seraphim, living creatures, and living beasts/beings.
Ex. 25:20 describes as having wings, and their prominence in Moses' Tabernacle and later in Solomon's Temple shows them especially associated with guarding the Mercy Seat at God's throne. The first time these angels are mentioned in the Bible is Gen. 3:24 where they are stationed as guards (with flaming swords) to keep Adam and Eve from going back into the Garden of Eden.
The are described in Isa. 6:2 as having six wings; two covering their face, two covering their feet, and two for flying. They are standing above God's throne praising Him; "And one cried unto another, and said, Holy, holy, holy, is the Lord of hosts: the whole earth is full of His glory." These may be the same as the living beings below.
Ezek. 1:5-14 describes angelic beings called "" that have the "likeness of a man." Likeness (resemblance) must mean they stand erect and are shaped like a human, because all resemblance stops there. Their head has four faces on it; a man's face on the front, a lion's face on the right side, an ox's face on the left side, and an eagle's face on the back of their head. They have four wings that allow them to fly forward, back, left, or right without turning their bodies. They have a man's hand under each wing, cloven feet like a calf, and they sparkled like burnished brass.
In Rev. 4:6-8 "four" (living beings) are reported to be around God's throne saying, "Holy, holy, holy, Lord God Almighty, which was, and is, and is to come." They do this day and night, without rest. These "beasts" have six wings, and are full of eyes, front and back. One of them has a face like a lion, one a face like a calf, one a face as a man, and the fourth a face like an eagle. These may be the same as the seraphim.
When angels have been visible on earth they have consistently appeared in human form (Gen 18:2, Dan. 10:18, Zech. 2:1); they protect God's people (Dan. 3:28, Matt. 26:53); and can deliver us from danger (Acts 5:19). When you read "The angel of the Lord" (i.e. Gen. 6:7-11), it's usually a reference to Jehovah, The Lord Himself before He came as a baby in Bethlehem.
Many believe the "sons of God" who took human wives in Gen. 6:1-4 were angels, or what Daniel calls Watchers, sent down to assist the humans. They took human wives and their offspring were called "Nephilim" in the Hebrew Pentateuch. They were wicked and had so corrupted the human blood-line that God sent the flood in Noah's day to destroy them. I believe the spirits of these Nephilim are the demons talked about in the Bible. These disobedient co-habiting angels are also possibly those referred to in 2 Pet. 2:4 and Jude 6. In Matt. 22:30 Jesus said "the angels of God in Heaven" do not get married. This could mean they don't reproduce (they are eternal so they don't need to reproduce) or it could mean they are not capable of reproducing because they are all males. Notice He said "those in Heaven," possibly implying there was a time when those not in Heaven could reproduce. This has been pondered about 2,000 years with no answer yet.