What is a lease agreement? The written contract that sets what a tenant pays, for how long, and what each side owes the other.
A lease agreement is the contract between a landlord and a tenant. It names the parties and the property, sets the rent and when it is due, fixes the term, records the deposit, and divides the duties: who pays which utility, who maintains what, what the tenant may and may not do, and how either side ends the arrangement.
Most of what people argue about later is decided by the parts nobody reads: late fees, notice periods, whether the deposit covers normal wear, what happens if the tenant leaves early. State law overrides the page on many of those, and it varies enormously, so a lease copied from another state can be unenforceable in the parts that matter most.
A month-to-month tenancy is a lease too. The difference is the term: a fixed lease runs to a date, a month-to-month renews until somebody gives notice, and the notice each side owes is set by state law rather than by preference.
A worked example
A twelve-month lease at $1,850 a month, due on the first, with a $1,850 deposit, the tenant paying power and internet and the landlord paying water and trash, and thirty days' written notice to end it at term. Everything argued about later is in that sentence or missing from it.
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Questions people ask
Does a lease have to be in writing?
For a short tenancy many states allow an oral agreement, but a lease for a longer term generally has to be written to be enforceable, and the rules differ by state. A written lease is worth having regardless: it is the only record of what was agreed.
What is the difference between a lease and a rental agreement?
In common use, a lease runs for a fixed term and a rental agreement renews month to month until somebody gives notice. Both are contracts and both are governed by the same state landlord-tenant law.