As you level your account up, you’ll receive lots of rewards and also buy lots of items in the shop. The inventory is the place to manage and equip them if you want. There you will find your characters, skins, portraits, sprays, start effects, death effects, rebuild effects and score effects.
In order to equip an item, you just need to select it and click on the Equip button. Items such as Sprays, Portraits, and Effects are account-wide, which means that they will be equipped for all your characters.