This is a great question to address. Lets start with the Ark of the Old Covenant; what was it? It was just a pretty box with some stuff in it right? Lets check out Exodus 25:
"You shall make an ark of acacia wood, two and a half cubits long, one an a half cubits wide, and one and a half cubits high. Plate it inside and outside with pure gold, and put a molding of gold around the top of it...You shall then make a cover of pure gold, two cubits and a half long, and one and a half cubits wide. Make two cherubim of beaten gold for the two ends of the cover, fastening them so that one cherub springs direct from each end...[and more details]"
Within this chapter we find that the ark was more than "just a pretty box," or at least God thought so. He laid out very detailed measurements for it and how it was to be made and the area it was to be kept. When finished it didn't just hold "some stuff," but three items: the ten commandments (Dt 10:2), the Rod of Jesse (somewhere in OT), and manna from the desert (Ex 16:34). It was this that was overshadowed by God and He dwelt among them.
Now when we consider the things that the ark held we see that they were all types of Jesus. Jesus is the true Manna come down from heaven of which we eat and never die (John 6). Jesus is the true high priest who offers the one sacrifice (Heb 4:14). And Jesus is the Word of God made flesh (John 1). Jesus is the fulfillment of the OT types, so one begins to wonder what the fulfillment of the ark is. What is it that was overshadowed by God and through which He became man and dwelt among us?
In Luke 1:35 we find the angel telling Mary "...The holy Spirit will come upon you and the power of the Most High will overshadow you. Therefore the child to be born will be called holy, the Son of God." Well, it would appear that Mary is a likely candidate for the New Ark of the Covenant, is there anything else to support this?
Yes! Luke continues with the travels of Mary, how she journeyed to the hill country to visit her cousin Elizabeth. At her greeting John the baptist leaps for joy and Elizabeth cries out "How should this be that the Mother of my Lord should come to me?" Mary remains there for three months and I'm sure brought blessings upon the house.
In the OT we hear the Ark's journey in the hill country (2 Sam 6). The ark was being brought away from the Philistines to Jerusalem when Uzzah reached out and touched it when he wasn't supposed to. Upon his death David cries out "How can the ark of the Lord come to me?" The ark is then taken to the home of Obededom and left there for three months during which it greatly blesses the household. At the end of this time David brings it into Jerusalem leaping and dancing before it.
The parallels are clearly there, is it enough? Is there anything else?
Well, the ark of the OC had exact specifications and was carefully made, without flaw. Christians (at least until after Luther) believed that Mary was carefully made by God so that she would be without flaw and a fitting dwelling place for God.
And finally we come back to Revelation and the Ark and the Woman. If we put ourselves in the mindset of the Jews of the time what would they have heard? That John saw a vision of the Ark of God! The ark that has been missing for years and is a powerful weapon of Israel, leading them in battles. How marvelous and exciting! What does it look like (is it as glorious as described)? Where is it? How do we find it? Oh how exciting!
Yet John doesn't describe it. He describes everything else, every other vision is full of eyes and wings and fiery wheels, but this vision that the Jews would have been drooling over to hear more gets only a couple lines? There is an ark and some loud thunder...quite a let down.
But if we remember that at the time the bible was written there were no chapter or verse dividers there is the possibility for more. Could it be that John is describing the ark when he describes the woman? "The Lord's temple is opened and you could see the ark within the temple, a woman clothed with the sun..."
This makes sense to me, but this isn't new teaching (if it were I would doubt it). There have been Christians throughout history who've seen this connection.
Athanasius of Alexandria (c. 296-373) was the main defender of the deity of Christ against the second-century heretics. He wrote: "O noble Virgin, truly you are greater than any other greatness. For who is your equal in greatness, O dwelling place of God the Word? To whom among all creatures shall I compare you, O Virgin? You are greater than them all O [Ark of the] Covenant, clothed with purity instead of gold! You are the ark in which is found the golden vessel containing the true manna, that is, the flesh in which divinity resides" (Homily of the Papyrus of Turin).
This is just a brief post, there are others who've written whole books on this topic (and done a much better job). Further readings: