Archangels and Cherubim are spirit beings who are at God's service and endowed with tremendous power and knowledge. They are collectively called angels, the host of heaven (1Kings 22:19, etc.), or "principalities and powers" (see Romans 8:28). Interestingly, the Bible only reveals the names of three such angels. They are Michael, Gabriel, and Lucifer.
The Bible refers to Cherubim (plural of Cherub) at least 30 times in the Old Testament, with the books of Ezekiel (12), followed the book of 1Kings (6), containing the most references. Archangels are directly referred to only twice, both of which are in the New Testament.
Because the Lord Himself shall descend from heaven with a shout of command, with the voice of an archangel and with the trumpet of God; and the dead in Christ shall rise first (1Thessalonians 4:16, HBFV).
But Michael the archangel, when he was personally taking issue with the devil, disputing about the body of Moses, did not presume to pronounce a reviling judgment against him, but said, "The Lord Himself rebuke you!" (Jude 9, HBFV).
Michael the Archangel
Michael is one of the three named spirit beings in Scripture. He is called both "one of the chief princes" (Daniel 10:13) and "your prince" (verse 21) and is one of the known Archangels. He has been, and will be, involved in major events around the world.
And there was war in heaven; Michael and his angels warred against the dragon, and the dragon and his angels warred. But they did not prevail, neither was their place found any more in heaven (Revelation 12:7 - 8, HBFV).
Gabriel
Gabriel, because he has also been involved in major Biblical events, is likely another spirit that is in this class.
And it came to pass when I, even I, Daniel, had seen the vision and sought to understand it, then, behold, there stood before me one having the appearance of a man. And I heard a man's voice between the banks of Ulai, which called and said, "Gabriel, make this one understand the vision." ( Daniel 8:15 - 16, HBFV).
It was Gabriel who gave Daniel the famous 70 weeks prophecy that revealed when the Messiah would appear (Daniel 9:20 - 21, 24). This Archangel ranked spirit being also announced the miraculous births of both John the Baptist and Jesus Christ (Luke 1:13, 19, 26 - 27, 31).
What Do They Look Like?
There is no description of what these spirit beings looked like. Although some speculate that Cherubim are the same as Archangels, there is no Biblical support for this belief. What seems clear is that both of them belong to a higher order of angels.
A representation of two Cherubim (but not Archangels) was placed, by God's command, on top of the Ark of the Covenant (Exodus 25, 37, etc.). They were still on the ark when it was moved to a very special place in Jerusalem's temple known as the Most Holy Place (or Holy of Holies), which is a replica of God's throne in heaven (1Kings 8:6 - 7, Hebrews 8:5).
The only time Cherubim appear away from God's throne is after the casting of Adam and Eve out of the Garden of Eden. The Bible seems to indicate that several of them were used by God to stop any attempt to re-enter the garden.
And He drove out the man, and He placed cherubim at the east of the garden of Eden, and a flaming sword which turned every way to guard the way to the tree of life (Genesis 3:24).
A description of what Cherubim look like does exist but does not offer more information. We do know that they have four faces and four wings (Ezekiel 10:10 - 12, 14). Lucifer, who because of vanity and sin turned himself into the devil (see Ezekiel 28:12 - 19), was originally one of this angelic class who are directly associated with God's throne (Ezekiel 28:14).
Conclusion
The Bible gives us precious, if any, information regarding angelic beings. While Michael and Gabriel are certainly Archangels, Lucifer was one of the Cherubim. It would be interesting to learn a bit more about these unusual beings. God, in his wisdom, has decided not to reveal much to man about the spirits he created.