The stories of the star, the wise men, the flight to
Egypt and Herod killing the children. These are all part of how Matthew
describes Jesus' birth.
Jesus as a teacher. There are five times in Matthew
where Jesus delivers instructions about how to live.
A concern about righteousness. See the discussion on
5:6 for examples.
The fulfillment of prophecy. This happens in the story
of Jesus' birth (for example at 1.22, 2.15) and throughout the gospel
(Matthew 12.17 and 27.9 are examples, and there are others).
Sometimes Matthew is called the "Jewish
gospel" for its concern about the Law. However, not everyone thinks
this is a revealing term for Matthew.