What significance, if any, does the doctrine of the eternal virginity of Mary have? I understand that the Catholic Church (and perhaps the Orthodox church as well) teaches that Mary is "the eternal virgin" Mary.  

If this were an important doctrine, it seems there would be fairly clear reference to it in the Scriptures.  However, the Bible is incredibly silent on it and even seems to indicate that Joseph had no union with here until Jesus was born.  


  When Joseph woke from sleep, he did as the angel of the Lord commanded
  him: he took his wife, but knew her not until she had given birth
  to a son. And he called his name Jesus.  Matthew 1:24-25 ESV


Admittedly, I don't believe Mary is the eternal virgin, and it seems by implication that Joseph would need to be an eternal virgin as well since he was married to her.  Nonetheless, in my understanding, it seems to me to be such a minute issue that it's hardly worth the effort to invest any significant amount of energy debating it.  Other things seem to be of far greater importance.

So, here's the question:

What importance does the eternal virginity of Mary have?  What does it matter?  A what would have been so horrible about her and Joseph enjoying the intimacy God provided for a married couple?
The importance of the perpetual virginity of Mary lies in the scriptural parallelism between Mary and the Ark of Covenant.

The Ark:


Journeys to a town in the hills of Judah (II Samuel 6:2) 
It is greeted with awe “How can the ark of the LORD ever come to me?”
(II    Samuel 6:9 KJV) 
It remains at the house of Obed-Edom for three months (II Samuel 6:11)


In the same way Mary:


Journeys to a town in the hills of Judah (Luke 1:39) 
It is greeted with awe "And whence is this to me, that the mother of
my Lord should    come to me?" (Luke 1:43)
It remains with Elizabeth for three months: "And Mary abode with her
about three months,  and returned to her own    house" (Luke 1:56 KJV)


I quote orthodox wiki:


  The Ark of the Covenant and the Mother of our Lord are in a sense two
  ways of looking at the same reality [...]


Because both are different manifestations of the presence of the Lord. Mary --who is a limited being-- carried in her womb the uncontainable --who is God incarnate: Jesus Christ. And in the same way that Jesus chose to lay his dead corpse in a new sepulcher (John 19:41), it is natural to believe that he also chose a "new" womb to come to this world.  

The belief in ever-virginity of Mary has been a long held tradition, even the protestant reformers held such belief. I won't go deep into the testimonies of the early fathers or the protestant reformers. 

A more extensive article can be read at orthodox wiki and at Newman Catholic Apologetics

EDIT

This answer would have been incomplete without addressing virgin birth. As article 499 of the Catechism explains, virgin birth and perpetual virginity are intertwined doctrines.

To gain some insight on perpetual virginity I'll decided to add an excerpt from an homily of St. Josemaria Escriva in which he explains the importance of the doctrine of perpetual virginity of Mary.


  You don't have to wait to be old or lifeless to practice the virtue of
  chastity. Purity comes from love; and the strength and gaiety of youth
  are no obstacle for noble love. Joseph had a young heart and a young
  body when he married Mary, when he learned of the mystery of her
  divine motherhood, when he lived in her company, respecting the
  integrity God wished to give the world as one more sign that he had
  come to share the life of his creatures. Anyone who cannot understand
  a love like that knows very little of true love and is a complete
  stranger to the christian meaning of chastity (Is Christ passing by, In St. Joseph Workshop)


Paraphrasing, Joseph decided not to know Mary as a sign that God had touched her.  I'll try to explain: Mary's perpetual virginity is important because it leaves a material imprint, an evidence of his coming to us. If we think that Mary was not ever-virgin, how are we so sure that Mary's first son is indeed the Son of God? On the other hand, if Mary is ever-virgin (as has been held for many centuries) we can readily admit that her first and only son was conceived by divine intervention.

In Catholic doctrine, Mary's perpetual virginity is a sign that God has come to us indeed.