[Aquinasfan]

In fact, it means that Mary herself was conceived free of sin before her birth circa 20 BCE.

As a non-Catholic, could someone please explain the reasoning behind this?

Thanks for asking. There are three main reasons that I know of (besides Tradition). The first is the fact that Mary is addressed in Scripture as "full of grace" or "perfected in grace." Secondly, through typology. Mary is considered the Ark of the New Covenant. In the Old Testament the Ark contained Aaron's staff (signifying the priesthood), the Ten Commandments (representing the Law) and the manna (the bread from Heaven). In the New Testament, Mary (the new Ark) contained Jesus, the eternal High Priest, the New "Law," and the new "bread from Heaven" ("whoever eats this bread will live forever"). Finally, since God's Word (the decalogue) was kept in the Holy of Holies, it seems to be analogously necessary that Jesus (the Word made flesh) would have to be contained in a holy vessel (sinless mother).

[JesseShurun]

Yes, and since it is in reality the Ark that saves, (as the lesson in the Noah story teaches ) Mary really should be worshipped then as the Savior. I just don't know why it's so hard for these scoffers to see this.