Calling Mary a mediatrix might sound exotic and even daunting. But mediatrix simply means, according to the dictionary, a woman who is a mediator!
Throughout Christianity, Mary has placed herself between her son and humanity, advocating or mediating for her children's wants, needs, and sufferings.
Mary puts herself in the middle, and in that way acts as a mediatrix. And she does this not as an outsider, but as Mother. She knows that in her mothering she not only can point out the needs of humanity to her son, but in essence she has the right to do so!
from The Complete Idiot's Guide to Mary of Nazareth by Maria Ruiz Scaperlanda (Alpha Penguin)