Its about a homeless teenager.
In the music video for "Nobody's Home", Avril plays a homeless teenager who lives street-to-street with another girl. Lavigne, who said it was really fun to make, had to wear a black wig, and acid-wash jeans for the video. The other side Lavigne had to play was a rich-like version of her: in a dress, with long, curled blonde hair, singing the song with an orchestra behind her.
"Nobody's Home" showed the outcasted, homeless Lavigne trying to get off the streets. She also tries to call her mother, but hangs up. In other parts of the video the outcasted girl is shown washing herself in a convenience store bathroom. She also tries playing the guitar on the street, probably trying to earn money. The video also shows the runaway trying to get inside an unlocked car during heavy rain. At the end of the video, the girl, dirty clothes, messy short hair and all, is shown with a tear rolling down her cheek. After that, she turns around and walks away.
Found this on wiki.