Gru comes from a long lineage of villain as shown with dozen of statues of his ancestors in Dru's hideout. Although his hometown is unknown, in an interview with Ellen DeGeneres he claimed he was from Albuquerque, New Mexico.
As a child he had always dreamed of going to the moon. He made a "prototype" rocket out of macaroni and an actual working prototype rocket. For most of his childhood he was neglected and ignored by his mother, and it is unknown if this is what inspired him to become a supervillain, or if the Gru family is a family of supervillains, although his mother showed no signs of being one.
He has worked with Dr. Nefario, who builds gadgets and weapons for Gru, for some time and based on what Dr. Nefario said, they have been planning the moon heist for a long time.