You will need inventory slots for the items you pick up, if all your slots are full you can free some up by selling items to vendors. This is done by going to The Hub (main screen), selecting the shop and choosing either Pedro or Big Red. If you interact with the owner and tap on 'Gear' and the 'Sale' option is on, you will be able to sell your items by tapping the item you want to sell and clicking 'Confirm'.
There are 12 total inventory slots you can equip items to: 1 head slot, 1 front slot, 1 back slot, 1 waist slot, 5 armor slots (shoulders, hands, torso, legs and feet), and 3 weapon slots. The front, back, head and waist slots are purely cosmetic and most items cost premium currency.