Lease dictionary
Assignment
Transferring your entire lease to someone else, who then becomes the tenant.
Assignment hands your whole lease to a new person: they take over the unit, the rent, and the obligations for the remaining term. It differs from subletting, where you stay on the lease and the subtenant answers to you.
Most leases require the landlord's written consent to assign. Some states say that consent can't be unreasonably withheld.
Watch out
Unless the landlord releases you in writing, you can remain liable if your assignee stops paying. Ask for a release, not just consent.