To dream of a backpack represents self-sufficiency. An area of your life where you are doing something on your own. It may also reflect problems that you have to deal with all by yourself. Doing your own thing.
A backpack may also represent hopes, desires, and secrets that you don't wish to tell anyone about.
Example: A woman dreamed of hiding a laptop in her backpack. In real life she was making plans to see a concert that her boyfriend didn't want to see. The backpack reflects her willingness to "go it alone" and make plans for the concert anyway.