A notice to vacate is the formal, written statement that a tenancy is ending. It runs in both directions: a tenant gives one to announce they are moving out, and a landlord gives one to end a month-to-month tenancy or decline to renew a lease. It is distinct from a notice to pay or quit, which is a demand tied to a lease violation — a notice to vacate for a periodic tenancy generally does not require a stated reason, though some jurisdictions with "just cause" rules do require one.
The load-bearing details are the notice period and delivery. How much advance notice is required varies by state and locality, by tenancy type, and sometimes by how long the tenant has lived there; the required delivery method (personal service, posting, mail) is often specified too, and getting either wrong can void the notice and restart the clock. Put every notice in writing with a clear end date, keep proof of delivery, and check your current local requirements before sending — the general shape described here is not a substitute for your jurisdiction's actual rules.
This is general educational information, not legal or tax advice. Rules vary by state and locality and change over time — check your local law and confirm specifics with a qualified professional.