Symbolism, Imagery, Allegory
When Lady Reason first visits Christine de Pizan, Christine is judging herself completely based on all the horrible things that men have said about women throughout history. But Lady Reason holds up a special mirror that shows things as they actually are, not just as people think they are. Good ol' Lady Reason.
As she says to Christine,
"My mirror has such great dignity that not without reason is it surrounded by rich and precious gems, so that you see, thanks to this mirror, the essences, qualities, proportions, and measures of all things are known, nor can anything be done well without it." (1.3.2)
When Christine sees herself in this mirror, she learns to see herself for what she truly is—a good person—instead of just seeing all of the bad things that men have said about her and women in general. In a sense, Christine wants this book to be like a mirror for her female readers, showing them the truth about just how good women can be.
This mirror also compounds our theory that Lady Reason is actually Albus Dumbledore. Pardon us while we geek out a sec—doesn't Lady Reason's mirror bear a passing resemblance to the Mirror of Erised? We bet you five bucks that J.K. Rowling read a little Christine de Pizan at some point in her illustrious career.