Editable Picklist

I'm trying to create a picklist that can be edited by the user. For example, I created a field called Business Unit. When the user creates/edits a Contact, they will need to choose which division (Business Unit), the Contact works in. How do I make it so if the user does not see the Business Unit value they require, they can simply add one to the existing picklist? I have also attached a photo of the Field Setup. Under Default Value and Id, I need these values to match the Picklist Values. In other words, I need the first picklist