Anakin Solo was the son of Han and Leia Organa Solo. Apparently after giving birth to twins, Leia was so addicted to certain parts of Han that she didn't care about the pain. While she was pregnant, Palpatine tried to possess her child. Anakin was overly emo because of this, and being named after his grandfather.
Behind the scenes
The rumor is that Darth Lucas had Anakin killed off so he wouldn't be confused with his grandfather. As a result, there is now a droid named Anakin Solo, and a Star Destroyer named the Anakin Solo. That's someone's way of saying "Fuck you, George."