This is for cash you are using to reduce your monthly payment. As an example, say you have $1,500 to put down. Then enter that here. But if you also need some of the $1,500 to cover your first month payment, then subtract that amount first.
Experts advise to not put money down on a lease and The BOSS agrees. Yes it will decrease your monthly payment. But it also gives the dealer another lever to pull in playing the monthly payment game.
Check this LINK for a more thorough article on the topic.