Security deposit
Money a landlord holds to cover damage or unpaid rent. For most New Jersey rentals it can't be more than 1.5 times one month's rent, it must earn interest that belongs to you, and it's due back within 30 days after your tenancy ends.
New Jersey example
Made-up numbers: your Hoboken rent is $2,000 a month, so the deposit can be no more than $3,000 (1.5 x $2,000). If your lease ends June 30, the landlord has until July 30 to return it with interest, minus any itemized deductions for damage beyond normal wear and tear. If the landlord wrongly keeps it, a court may award you double the amount withheld.
Official source
This is a plain-English summary. Rules and dollar amounts change, so check the official source or a professional before you file or sign anything.