Short answers, pulled from the story.
The main characters include middle school student Madoka Kaname, her best friend Sayaka Miki, transfer student Homura Akemi, upperclassman Mami Tomoe, and veteran magical girl Kyoko Sakura. They encounter a cat-like creature named Kyubey who offers them contracts to fight witches.
Magical girls form Soul Gems which serve as the source of their magic and give up their souls to create these gems. When a Soul Gem becomes too tainted with despair it turns into a Grief Seed that hatches into a witch.
Puella Magi Madoka Magica debuted on Mainichi Broadcasting System, Tokyo Broadcasting System, and Chubu-Nippon Broadcasting in Japan on the 7th of January 2011. The first ten episodes aired weekly without interruption before being halted due to the 2011 Tōhoku earthquake and tsunami.
The total sales of BD and DVDs exceeded 600,000 copies as of October 2012. The first volume sold 53,000 copies in its first week while the second volume sold 54,000 copies breaking previous records.
Shaft developed a three-part theatrical film project announced in November 2011. The first two films were released in theaters on the 6th of October 2012 and the 13th of October 2012 covering the eight and four episodes respectively.