Some associate these 4 bests with the 4 Gospels written about Jesus (Matthew, Mark, Luke, John)
This can give us an idea of why there 4 Gospel books written about Jesus, rather than just one. Each author of these 4 books was coming from a different viewpoint about Jesus in his writing.
The 4 beasts are said to correlate to the 4 views of Jesus in the Gospels.
I Revelation 4:7 we see what the beasts are "The first living creature was like a lion, the second living creature like a calf, the third living creature had a face like a man, and the fourth living creature was like a flying eagle."
The Gospel according to Matthew is said to be represented by the Lion. A lion most often represent royalty, and even today is often seen as a 'king' to animals. This Gospel contains a genealogy of Jesus from Abraham, through the line of King David. It is presenting his right to David's throne.
The Gospel according to Mark is said to be represented by the calf (also referred to as an ox. This shows Jesus as a servant to humanity, as an ox is. There is no genealogy found, but instead the book starts with Jesus' baptism, and his ministry. This was his service while on earth.
The Gospel according to Luke is said to be represented by the man. Luke portrayed Jesus as human. The genealogy in this book was traced back to Adam, showing Jesus was indeed a man, although completely perfect unlike the rest of us.
The Gospel according to John is said to be represented by the flying eagle. This book portrayed the divinity of Christ more than any of the other 3, even beginning by explaining that The Word was with God, was God, and became flesh. The eagle is seen as one of the most majestic birds, being able to fly at great heights.
I have more that relates to the 4 Gospels, but what I put was the only part relevant to the beasts. I can add more later if anyone is interested.