Being an apostle means being a conduit, a teacher not about one's self but about the subject one is announcing. One does not point to oneself as the message and for that reason apostles are often remembered not for who they are but for what they did.
In the synoptic Gospels, Andrew is merely the brother of Peter (except in Luke where he does not even get a mention though he makes up for that in Acts), a fellow fisherman with (depending on the Gospel) the partners of Peter who have the pleasure of being Zebedee's sons. So, much like most of the Twelve, as important as he is as one of the Twelve, Andrew does not have much said about him. Perhaps it is the nature of apostleship and the communities of the Gospels affected by specific apostles as they went on their way teaching about Jesus.
But, we get glimpses. He is close enough to Jesus (and enough like his brother Peter) to question Jesus when he sits before the hungry crowd and invites the Apostles to feed the them, and to ask Jesus about his teachings on the destruction of Jerusalem.
But in John, it is different. In John it is Andrew who follows John the Baptist and to whom John points out Jesus. It is Andrew who introduces Peter to Jesus; later Andrew brings Greeks to see Jesus (though it never says they met him - I wonder if they are still standing by the door waiting...). John shows him as the perfect apostle - he points others to Jesus. He does not lord it over others, is not caught in a self-centered, smug knowledge. He is wrapped up in a joy that bursts forth and seeks out others to share it. May we too be apostles, humble enough to put Jesus first and selfless enough to be eager to share him with others.
As Jesus was walking by the Sea of Galilee, he saw two brothers, Simon who is called Peter, and his brother Andrew, casting a net into the sea; they were fishermen. He said to them, "Come after me, and I will make you fishers of men." At once they left their nets and followed him. He walked along from there and saw two other brothers, James, the son of Zebedee, and his brother John. They were in a boat, with their father Zebedee, mending their nets.
He called them, and immediately they left their boat and their father and followed him.
-- Matthew 4:18-22