Tenancy is the act of living somewhere, especially in a house, building, or apartment. You could say, for example, that your tenancy in the little white farmhouse lasted for six years, until you moved to the city.
The noun tenancy means a period of living in a certain place or having a business in a specific building. If you give up your tenancy, you move to a new place, and if your tenancy ends earlier than you expected, you may owe your landlord some money. The word tenancy is closely related to tenant, with its earliest meaning of "one who holds land," from a Latin root — tenere, "to keep" or "to hold."