The Languages Reference contains the available languages that are available to be set as "Preferred Language" in the Patient Tab. You cannot add or remove Language References.
By selecting a particular Language Reference, you can identify the ISO 639 codes in the appropriate fields that are tied to this Language.
The "Show in Lists" checkbox allows you to add or remove the currently selected Language from the available options when selecting a patient's Preferred Language. If you need to enable a particular Language, first locate it in the sidebar, then click the "Show in Lists" checkbox. Don't forget to save by pressing Command-S.