Yo, yo, yo...Wassup, my peep?
Mary isn't worshipped. It kinda goes like this:
God,
Jesus
................................................(Holy Spirit)................
Mary (the greatest of saints)
the rest of the saints
But Mary is a very big deal (some theologans study Mariology - the study of Mary - almost exclusively). Mary is considered by the church to be a part of the faith. Marian teaching is not a supplement to doctrine that is complete without her. As she was the mother of Christ, we kinda see her as the mother of Christianity. But they had meetings and decided she isn't the formal Mother of the Church, rather a most loving mother. But catholics, including the former pope, see her that way, and believe her to be so. We are all kinda her children, like we're the children of God (although God IS the Father).
Catholics have six "Holydays of Obligation," which are days we have to go to church that aren't necessarily Sundays. Three of them are Mary related: January 1 (The Solemnity of the Mother of God), August 15 (The Assumption), December 8 (the Immaculate Conception). November 1st is All Saints Day, and since Mary is a saint, she's kinda involved there, too.
Mary (full of grace) exemplifies faith, hope, love of God, and generous concern for others. Because Mary agreed to the whole Immaculate Conception deal (Annunciation, consenting to Incarnation), Jesus was able to be born, which gives her divine motherhood status. When Jesus says, "behold your mother" it is taken to mean she's kinda mother to everyone. She's taken (body and soul) to heaven, where she continues to intercede for all her children.
Someone mentioned Mary and women. No doubt women look to her more. Because of the life she led, she is an inspiration in her devotion to God and then to Jesus. The single, married, and widowed can all be inspired by her.
What you say about the bible? I dunno WHAT the bible says about talking to, or praying to, dead people, because (of course) I don't read it. I'm guessing it makes an exception for Jesus? And I'm hoping it makes an exception for parents / grandparents (?).
But, anyway, we pray to Mary and the Saints. They aren't worshiped as God is, but are revered and respected. They aren't just regular people to us.
I'm not trying to "sell" anyone on Mary or the rest of the saints. It's a Catholic thing. And I did my best to explain it.