Symbolism, Imagery, Allegory
The most important saint in Roman Catholicism, Mary miraculously becomes the mother of Christ while remaining a virgin. Seen as the mother of God, she is a symbol of how a woman can have dramatic, even supernatural, power. In other words, Mary is a biblically-backed symbol of the incredible power women are capable of possessing. And in a time when women are pretty much stuck in second-class citizen status, Mary is an acceptable—and rare—symbol of power for Joan to align herself with.
Because Joan is freaking powerful. She dominates in battle, not only stepping into male turf but pretty much owning it. But despite this undeniable strength, due to the unusualness of her presence, she still needs a little back-up. And while women today might turn to other women who've come before them in their field (or on the field, as the case may be), Joan doesn't really have that available to her. So she cleverly identifies herself with Mary, suggesting that her supernatural power comes from the Virgin.
The Virgin Mary, then, represents both Joan's power and the lack of other powerful women. She also, however, represents French Catholic culture at this time, a culture the British were none too keen on. And because of this distaste on the part of the English, the Virgin Mary is also a reminder of the limits of Joan's power. She may blow the Dauphin's mind, but in the end the British aren't having it, and they capture her and burn her at the stake with no concern at all for how the Virgin Mary might feel about this development.