Matthew, the gospel writer was a Levite, and therefore he presented Jesus as the Messiah of Israel, the Lion of Judah. He was mostly concerned with what Jesus said, and was writing for a Jewish audience. His gospel is symbolised by a Lion.
Mark was writing the gospel from Peter’s eyewitness account and presented Jesus as the suffering servant, of whom we hear in Isaiah 53. He is concerned with what Jesus did, and was writing for a mainly Roman audience. His gospel is symbolised by an Ox.
Luke was the only Gentile writer, and presents Jesus as the Son of Man. He was concerned with what Jesus felt, and was writing mainly for the Greeks. His gospel is symbolised by a Man.
John presents Jesus as the Son of God. He is concerned with what Jesus was and is, and his gospel account is symbolised by an Eagle.
The creatures that represent each of the gospels were the ensigns for the camps of Israel, and are also characterised by the cherubim who worship God in Heaven (Ezekiel 1:10).
Thanks to Uncle Chuck Missler