In one sense the backpack is an item that is used to carry things. You can carry all kinds of belongings in a backpack, and some people that go on long international trips choose to carry solely a backpack as a means of storing all of their own good. However some people choose to merely use a backpack as a means of transporting student items. If you are in high school or college there is a good chance you will use one. Therefore one way of looking at the backpack in a dream is as a tool for carrying things as it is seen in daily life for the most part.
The other way of viewing a backpack is that of a simple weight on the shoulders. As helpful as backpacks can be they can also be harmful in causing damage to the shoulders and back from spending too much time carry heavy goods back and forth using the backpack as a means to do so. Therefore when dreaming about a backpack, it can also have a connection to putting too much pressure on your shoulders. These two different ways of looking at backpacks in terms of a dream symbol shed light on the different interpretations that could come up of dreams that involve backpacks.
One interpretation of a backpack, which involves you seeing the backpack as a tool for carrying goods for you, is that you are packing up and leaving something behind. This is not to say that you are forgetting something but rather purposefully choosing to leave a place that is in some way in disagreement with you. You want to get out of the situation that you are in and are packing up the parts of your life that are most important to you in order to make your escape from an oppressive environment. Perhaps there is just something that you want to forget. This too could lead to you dreaming of backpacks. It means there is something that you need to pack up for, some kind of journey (which could be physical, spiritual, or emotional) that you are going to undertake soon.
Another possible meaning of a dream that involves a backpack is that of responsibility. The backpack symbolizes all of the weight that is being put upon you. This could be a physical weight as in physical duties such as work that are being added to your schedule and taking up all of your time to think and to be yourself. It could also take the form of mental weight. You are being given too many different ideas and perspectives and have no way to sort through them. People are entrusting you with too much of their personal baggage and you are trying to bear the weight. Do not let anyone take advantage of you. Try to maintain your autonomy.