Short answers, pulled from the story.
Kyubey is an extraterrestrial being known as an Incubator and the mascot of the anime series Puella Magi Madoka Magica. He is a member of a hive-minded species that has been observing Earth for eons and uses technology to convert emotional energy into usable power.
When a girl makes a contract with Kyubey, he extracts her soul and places it inside a gem called a soul gem while reconstructing her body into a shell. The true nature of this transaction is hidden until the consequences become undeniable, leaving the girl with a soul trapped in a gem and a body that is merely a shell.
Kyubey approaches young girls specifically because this demographic produces the highest amount of emotional energy. The Incubators use this emotional energy to stave off the heat death of the universe and view the creation of witches and magical girls as a utilitarian necessity.
When a magical girl's soul gem becomes corrupted, it turns into a grief seed which is the peak of energy production. The magical girl then transforms into a witch, creating a cycle of destruction and energy generation that the Incubators utilize.
In the 2013 sequel The Rebellion Story, Kyubey attempts to seal Homura Akemi outside the Law of Circles jurisdiction to force Madoka Kaname back into the physical world. The plan backfires when Homura steals Madoka's powers, and Kyubey is last seen lying on the ground disheveled and shivering.
Kyubey won the 1st Newtype Anime Awards for Best Mascot Character in 2011 and the 2011 Net Buzzword's Bronze Prize for his popular catchphrase. Emiri Katō won the 6th Seiyu Awards for Best supporting actress in 2012 for her portrayal of Kyubey.