This unnamed boy is Penny's nephew, so he's possibly the son of Penny's sister and her shot husband, and also the nephew of Penny's brother. He has never appeared on the show, but has been mentioned a couple of times.
It was revealed in "The Hofstadter Isotope" (S02E20) that he is 13 years old. Penny wants to buy him a comic book and follows the gang to the comic book store. She buys the comics recommended by Stuart.
Her father Wyatt did mention that he didn't want his grandchildren who had to live in a house with wheels, so does his grandson live in a mobile home?