For He will command His angels concerning you to guard you in all your ways. On their hands they will bear you up, lest you strike your foot against a stone. (Psalm 91:11-12 ESV)
Angels are created beings who serve God. In Genesis 1:1, the Bible says that God created the heavens and the earth. In creating the heavens, God also created the hosts that inhabit His eternal dwelling place. When God appears to Job at the end of his ordeal, He asks him,
“Where were you when I laid the foundation of the earth? Tell me, if you have understanding. Who determined its measurements—surely you know! Or who stretched the line upon it? On what were its bases sunk, or who laid its cornerstone, when the morning stars sang together and all the sons of God shouted for joy?" (Job 38:4-7 ESV)
Angels are referred to in Scripture as "morning stars" and "sons of God", so God indicates to Job that angels were there with Him when He created the earth.
When angels appear to humans in the Bible, they take various forms. The angels who destroyed Sodom and Gomorrah appeared to Abraham as men. Gabriel appeared to both Zachariah and to Mary in his angelic form. The hosts of heaven were seen by Elisha's servant as an army of chariots of fire, surrounding the Syrian army that had surrounded the town of Dothan where they were staying.
In Scripture, only three angels are identified by name. The archangel, Michael, and his angels overcame the dragon (Satan) and his angels in the great war in heaven when Satan rebelled against God (Revelation 12:7-9). Gabriel appears to Zachariah to announce the birth of John the baptist, and to Mary to announce the birth of Jesus (Luke 1). And Lucifer, the Morning Star, is the angel who tried to take God's place and was thrown down from heaven, becoming Satan (Isaiah 14:12-14).
Angels have three broadly defined roles in Scripture. They are God's army - the host of heaven, battling the devil and his angels in the great spiritual war that is going on behind the scenes of our existence. They are messengers to human beings, as in the case of the angels who visited Abraham and Zachariah and Mary. And they are ministering spirits who attend to God's people, as it says in Hebrews 1:13-14:
Are they not all ministering spirits sent out to serve for the sake of those who are to inherit salvation?
Given what the Bible says about angels, there have also been misconceptions and exaggerations about them in human thought and art. It is pretty commonly believed in our culture today that people become angels when they die. But the Bible does not say that at all. Angels are a separate order of creation, and humans become glorified image bearers of the living God when we die and receive our eternal bodies. There is no depiction in scripture of angels as either beautiful females or chubby babies, as they are often depicted in art. Rather they are God's warrior host. And the fallen angels, demons, are to be respected since angels are inherently more powerful than human beings, but they are not to be feared, because in the name of Jesus believers have authority over them.
The role of angels in scripture is commonplace and secondary. They are God's servants, and they are not the center of the story of redemption the Bible tells us from cover to cover. Redemption is about God's amazing love and grace for is fallen, broken children (us human beings) who were created "a little lower than the angels" and gloriously in His own image (Psalm 8:5 and Genesis 1:26-27). Angels watch in wonder and assist God in battling evil and ministering to God's people. John 3:16 does not say "God so loved the world that He gave us angels to watch over us." He did something far greater. He gave us His one and only Son. Angels are not the center of the story. Jesus is.
Psalm 91:11-12 says that God commands His angels to guard us. But neither there nor in any other text in Scripture does it directly say that each person has a guardian angel assigned to them to protect their lives. Angels guard humans, whom God loves. Perhaps that is an even bigger promise than the concept that an angel watches over each one of us.
Many people have had the experience of being guarded by an angel or receiving a message from God through a person who randomly appears and suddenly disappears in an emergency situation. I believe God still sends angels to encourage and protect us. But the point is not to seek angels. The point is to continually seek Jesus. He might well send angels into our lives. He certainly sends the Holy Spirit to indwell our lives. And He will redeem our lives fully from sin and death to live with Him forever once we die physically.
To God be the glory!