Apartments, especially new ones or those having problems filling vacant units, sometimes offer one or two months free as a promotion. Other apartments sometimes offer lower deposits for new tenants.
Even if an apartment offers one free month, this might occur at the end of the lease, so prospective tenants might need to have enough to cover the first month before moving in. In addition, these deals are generally only for new tenants, so tenants likely need to pay each month if they renew for another lease. Apartments that offer discounted deposits often require that the prospective tenant have a good credit score and a good report from a previous landlord.