Yes a backpack can be used and brought on the plane as a personal item or carry on item.
Anything that fits under the seat of an airplane can be brought onto the plane with you as a carry on item or personal item.
The things that are considered to be carry on items or personal items that fit under the airplane seat are laptop bags, small duffel bags, hand bags, purses, pocketbooks, briefcase, laptop computer whether it has the case or not and diaper bags.
As long as the bag or item fits under the airplane seat with ease and fits the dimensions then you can bring it on the airplane.
However you're limited to certain amounts of those personal items that you can bring on the plane as a personal item or carry on.