The Emergency Contact Type Reference stores the options when selecting a Relationship to Patient to Emergency Contact records on a patient's chart. You can add these records in the Emergency Sub-Tab in the Patients Tab of the Patients Ability.
Emergency Contact Types are codified, meaning you cannot create custom types. However, you can add additional Emergency Contact Types by clicking the Green Plus in the sidebar. In order to use a newly added Type, you'll need to set a Codified Relationship from one of the available options for that type in the Codified Relationship drop down.
You can learn more about the Emergency Tab Here.