SPOILERS Alert : Spoiler details may follow
Main Article : Homura Akemi
Prior to the main story, Homura was a weak willed, shy, and clumsy who has no confidence in anything she does, but her first encounter with Madoka Kaname has given a boost in her confidence.
After the Walpurgisnacht battle on the first timeline, she made a contract with Kyuubey and she became a Puella Magi with time travelling powers, bringing her back to the past before she is discharged from the hospital. Thus looping the whole process.
While at first she had problems with settling down as a Puella Magi, but as she gain experience, her powers became stronger from time to time. Even so the first loop ended up a disaster and Madoka turned into a witch in the end. Before she could see the end, her second loop brought her back to the time same as her first loop, and Homura realized that everyone has been tricked, including herself. She tried to alarm the rest of the Puella Magis about it, but no one believed in her, until Sayaka Miki turned into Oktavia von Seckendorff, which despaired the rest of the Puella Magis : Kyouko Sakura murdered by Mami Tomoe who went crazy due to the revelation, which in turn killed by Madoka who saved Homura from getting killed by Mami.
The second loop ended with both Homura and Madoka almost turning into a Witch, but at the last minute Madoka saved Homura by purifying her Soul Gem, while at the same time leaving her one and only request to Homura.
Homura completely changed herself with the third loop due to the trauma, and became jaded...
Before episode 10 she was considered by the fans to be mysterious, cool beauty. But episode 10 soon shocked the fans by introducing a meek yet cute and different version of Homura to the viewers. Since then, tons of fanarts have appeared in pixiv due to the drastic change between the two characters, raising the popularity of the character even further than before.
The character also span two different pairings to the characters, Homu×Homu(ほむ×ほむ) and HomuMadoHomu (ほむまどほむ), and many fanarts are produced for it.