Age: 14
Birthdate: October 3
Zodiac: Libra
Height: 152 cm
Blood type: A
Shoe size: US Women's 5.5

A 14-year-old girl whose life changes when she encounters the Puella Magi Homura and the familiar Kyubey, who offers to transform her into a Puella Magi herself. She sees herself as a person without special qualities or talents, and after seeing Mami fighting against witches, wants to be a wonderful and cool Puella Magi like her. She is a rather selfless girl who wishes to be a magical girl simply so that she can help others. She allegedly has a large amount of magical potential within her.

Following Mami's death, she becomes uncertain about becoming a Puella Magi, becoming more so as the dark secrets of the Puella Magi are revealed to her. She is kind, gentle, averse to fighting, and wishes that everyone would get along, sometimes even putting her own life at risk to help others. In previous timelines that Homura had experienced, Madoka had become a Puella Magi, wielding a magic bow and arrow. According to Kyubey, she is capable of becoming the strongest Puella Magi and the most terrible witch, capable of destroying the world, which is why he is most interested in forming a contract with her.
At the beginning of the 3rd movie she is trapped inside Homura's tainted soul gem, in false Mitakihara. Her memories are gone and she is fighting "Nightmares" with the other 4 girls. During the finale, she regains her memories and godlike powers, but they are partially stolen by Akemi Homura to rewrite the world where Madoka can live as a human while Law of Cycles is still working. Her (and other magical girls') memories are rewritten by Homura, and in that world Madoka is the transfer student, who is greeted and guided by Homura.
(Source: Wikipedia)