Ezekiel 1:4-6,10 (NIV)
I looked, and I saw a windstorm coming out of the north--an immense cloud with flashing lightning and surrounded by brilliant light. The center of the fire looked like glowing metal, and in the fire was what looked like four living creatures. In appearance their form was that of a man, but each of them had four faces and four wings.
Their faces looked like this: Each of the four had the face of a man, and on the right side each had the face of a lion, and on the left the face of an ox; each also had the face of an eagle.
Ezekiel is sitting or the bank of the river, and this incredible vision from the Lord comes to him. It is a vision of the Glory of the Lord riding around in some sort of strange, mobile flying contraption (forgive me for using such a term in connection with a holy God, but that accurately describes the picture I get) with wheels. Somehow, this portable throne of God is attended to by angelic creatures as described is the above verse.
The faces of these four creatures are described as that of a lion, an ox, a man, and an eagle. These four images are a reminder of the fourfold mission of Jesus when he came to this earth.
First He came as a king, symbolized by the lion. This is the perspective from which Matthew wrote his gospel. Matthew was a Jew expecting his king and he authenticates Jesus right to the throne of David by giving his genealogy through Joseph and King David back to Abraham.
Secondly, Jesus came as a servant, symbolized by the ox. Mark was a Roman, whose only understanding of gainful employment in his culture was that of a servant. A servant has no pedigree and so needs no genealogy which Mark did not supply is his gospel account.
Thirdly Jesus came as a perfect man who never sinned as portrayed by Luke, the Greek physician. Luke demonstrated Jesus' sinless humanity by giving his lineage through his mother Mary all the way back to Adam, the first man. In bypassing the seed of man being born of the seed of woman, Jesus was fully man yet untainted by the sin nature we inherit from Adam.
Finally, Jesus came as God in the flesh. The eagle represents Jesus' deity. John wrote a genealogy in his gospel too. "In the beginning was the Word, and the Word was with God and the Word was God."
This same sort of vision of the throne of God is found in the book of Revelation:
Revelation 4:6-8 (NIV)
In the center, around the throne, were four living creatures, and they were covered with eyes, in front and in back. The first living creature was like a lion, the second was like an ox, the third had a face like a man, the fourth was like a flying eagle. Each of the four living creatures had six wings and was covered with eyes all around, even under his wings. Day and night they never stop saying: "Holy, holy, holy is the Lord God Almighty, who was, and is, and is to come."