In Borderlands 3 weapons in your inventory have the ability to be further customized with Trinkets. These trinkets can add a bit of personality to the weapon you are using and don’t really add any functionality to your guns.
To equip Trinkets you will need to heading into the Character Menu and tab to the backpack icon to see your inventory. You will then see the list of equipped weapons. The small box to the left of the gun is your trinket slot. Once you have a weapon highlighted either press left on the d-pad or the left stick to access this small box. Press A/X to access your available trinkets which will pop up on the right hand side of the screen.
Select which trinket you want to equip from this list and then press A to confirm. Once you’ve equipped your trinket you will be able to see it dangling from the weapon. These trinkets are small and located in different spots for each type of gun.