Your character would not be able to carry anything if not for bags. While each character automatically starts with a backpack, they also have 4 bag slots on their person and more in their bank.
A new character will have an empty set of bag slots. These can be found in the lower-right corner of the screen, just to the left of the backpack. When a character acquires a bag they want to use to help carry more equipment, they should drag the item icon to the bag slot. The player can then click on the bag to open it for additional storage space. Clicking into a slot also works, but only if the bag slot is unoccupied. Dragging will replace the old bag if there was one.
A character's bank space holds 32 [1] slots for items. However, as a player becomes involved heavily in questing, extra sets of gear, and all kinds of tradeskill items, more space is usually required. There are 7 purchaseable bag slots that allow the player to place a bag in them just like the personal inventory space.