The general assumption among source critics is that Mark was the first written gospel. This is seen by an analysis of Matthew and Luke — both Matthew and Luke have material in their gospels that is common to the gospel of Mark. At the same time, there is common material found in Luke and in Matthew that is not found in Mark. The scholars then try to account for this common information found in these two gospels that is absent from Mark's gospel. The working hypothesis is that Matthew and Luke, in addition to having Mark as a source for their information, had a second independent source that Mark did not use. This second independent source is called simply the "Q-source."
That letter Q is used since it is the first letter of the German word quelle, which is simply the word for source. That is to say, the Q-source is a source that is unknown to us but known to the gospel writers Matthew and Luke. Much of this analysis is speculative and hypothetical. Scholars differ as to whether the alleged Q-source was a written source shared by Matthew and Luke, or simply an oral tradition they both had access to. Wherever we land in our conclusions about the method by which the gospel writers compiled their texts, the very analysis that we have seen gives us one clear benefit. By isolating material that is found in Matthew and only in Matthew, or isolating material that is found in Luke and only in Luke, or isolating material found in Mark and only in Mark, we get clues as to the audience to which the author was directing his information and also his major themes in the particular gospel.
For example, in looking at the gospel of Matthew, we find more citations and allusions to Old Testament Scriptures than in any of the other gospels. This fact alone lends credence to the idea that Matthew was directing his gospel primarily to a Jewish audience to show how Jesus, the long-awaited Messiah, fulfilled Old Testament prophecy.
Excerpted from "The Witness of Matthew" by Ligonier Ministries (used by permission).