There are 4 Marian official dogmas
- She is conceived without original sin
- She is the Mother of God
- She is perpetually a virgin
- She was assumed into Heaven at the end of her earthly life
This all leads up to the 5th (unofficial) Marian dogma, which is what you're talking about
- She is the mediatrix of all graces
This is not doctrine, but it what many Catholics and popes (like Leo XIII) have proclaimed and believed. It is a hard concept even for me, but I think it makes sense. Mary is the Secondary Cause of our redemption. (See TAN Books "This is the Faith") Certainly God made her special, only the most special human being in history could bear God. But God also chose her, she had found favor with God.
We Catholics are not obliged to pray to Mary at all, just believe the infallible doctrine. But, by and large, we have a tradition of honoring her and believing that she has a strong intercessory power (See wedding at Cana) and that we should take her into our house (Like John the Apostle).
It's tradition and in general you could leave it at that. But the reformation broke with the tradition insisting on the bible as the sole source of God's truth, so we must defend our Blessed Mother and recapitulate what we already knew.
In the old testament she is prefigured by Eve (Mother of all the living), Sarah (Bearer of the new covenant), Ruth and Rachel (A sorrowful wife/mother).
She is the woman who's offspring would crush the serpent's head and she is the woman in Revelation clothed in a sun with a crown of stars. (Read the history and significance of the miraculous medal)
She is the model of piety and the embodiment of the Church (she literally was a tabernacle). (See Mary as the new Ark)
She has appeared in visions to mystics throughout the history of Christianity. Bringing messages of repentance and leading millions to worship to Jesus. (see Carl Anderson's, Head of Knights of Columbus, book on Our Lady of Guadalupe and all the converts)
She said yes to God.
She's my mother and yes, she took me from a child in the faith to a man when all my friends and relations strayed from the path.