An E106 covers you and your dependants living in another member state by affiliation to its national health service.
The E106 certificate is a certificate of entitlement to sickness/maternity benefits for persons going to live (not work) in another Member State. When the E106 is registered, the person and registered dependants can receive medical treatment on the same basis as an insured person of the Member State of residence. Within the EU, the application by the local authorities differs, and it is worth checking what the individual country requirements are in each circumstance. For example, in Ireland, E106 holders and their dependants normally receive a medical card as well. In most regions of Italy, an E106 is not necessary, apart from Milan where it is required, although you must have a European Health Card.
The E106 is also required in some countries by workers in addition to the E101 and European Health Card.