Security Deposit
A security deposit is money a tenant pays at move-in that the landlord holds until the lease ends. It covers unpaid rent and damage beyond normal wear, and the remainder is returned after move-out. State law sets how large it can be and how fast it must come back.
A deposit is separate from the 3x rent rule. Three times the rent describes the income you must show, not an amount you pay. Move-in costs are normally the first month of rent plus the deposit.
The two meet when an applicant falls short on income. Some landlords approve the lease in exchange for a larger deposit. That only works where the state cap leaves room, since many states limit deposits to one or two months of rent. See renting without 3x income.