Person custom fields allow you to assign an existing user in your organization as the value in your custom field. They can only be used as dropdowns.
To add a person custom field, go to Settings > Custom Fields > select the object you want to add it and click on Add new custom field:
From the menu, select Person field:
Give the Custom field a Title, description and click on Create Field.
Here is an example of how that custom field looks like when created under a Task: