The Gospel symbols are based on the biblical imagery found in Ezekiel and Revelation.  

The image of a man or angel represents the Gospel of Matthew and signifies Christ's human nature.  

The lion represents the Gospel of Mark and is a traditional symbol of royalty and power and, therefore, denotes Christ the King.

The ox or calf, the sacrificial victim, represents the Gospel of St. Luke and highlights the priestly character of Christ's mission.

The eagle stands for the Gospel of St. John, the evangelist "who soars to the heavens," because his theology is much more developed than the three Synoptic Gospels.  Just as an eagle soars above the earth, so John's theology soars above the other Gospels.

The symbols for the Synoptic Gospels probably come from how each one begins.  The Gospel of Mark begins with the lines:  "A voice cries out in the wilderness."  In the wilderness you can hear the roar of the lion for miles around.  Matthew's Gospel opens with the genealogy of Jesus, and represents Jesus' human roots.  The Gospel of Luke opens with the story of Zechariah the high priest, who offered a sacrifice of a bull on behalf of the nation.

These symbols were developed as a way of helping people to remember the different Gospels and the perspectives that they took, especially at a time when most people could not read.

Source:  En Theos -- Enthusiasm for the Faith
                Father James Gaffney; Pottsville, PA