A notice to quit refers to a specific type of notice given by a landlord to their tenant that explains that the tenant must vacate the property. Generally, a landlord must give his or her tenant at least three days notice before the tenant is legally obligated to leave.
A landlord can give his or her tenant a notice to quit for a number of different reasons. The reasons are generally reasons that violate the signed lease such as keeping pets in a place where pets aren't allowed, destroying property, or other problematic behavior. Landlord / tenant law varies from state to state. A notice to quit is an eviction.