Required

This field is used indicate whether a value must be populated for a particular user defined field when adding or updating a record.

If the Show in UI field is configured to not display the field, this indicator is ignored when entering data via the UI (however, it would continue to be enforced on any relevant import).  

When indicating a field is required, the system will validate at that point in time that the particular field contains an appropriate value for every record in that table, and will not allow you to define the field as required if a value is not currently supplied for every record.  To assist with the setup, when clicking on the Required field, you will be provided with a "Set empty values to" field, which will allow you to both specify that the field is required AND provide you with a means to supply a value for any field not currently populated.  Note that this value is not a default value that will be provided as new entries are created, but rather simply a one-time option to populate any empty records as you are defining this UDF as being required.