The bag is where you keep all the items you buy or find. It is divided into six tabs, plus an additional ALL tab. Each tab is for a different Category of item: Equipment, Use, Materials, Flesh, Gifts and broken. Some items are located under multiple tabs, although one of those tabs is usually either Material or broken.
The bag has a maximum capacity; each item takes up one point, and when the point level reaches the max you can't pick up any more items. You can increase the max limit by giving Elena certain gifts. These gifts are: quality metal, tanned leather and leather belt. She will sew them onto your bag the first time you give them to her.
However, if you need more room or simply don't want a certain item broken in the Towers, you can transfer these items (except Flesh) to the trunk.