The answer is a backpack. The term bagpack is a common mishearing that has now become slightly accepted in society. Bagback is not even a word although you could separate the word into bag pack, this still is incorrect. A backpack is a strapped bag with either one or two straps that sit on your shoulders. Some backpacks have waist support, these are particularly useful in heavy bags used in hiking and trekking.
The first known use of the word backpack was in 1897, although it appears that backpacks had been used previously to this date. Developed for military use these bags have been adapted for hiking, fashion, college, and travel in modern times.