They match your savings account for a downpayment, and help prove you'll be a good buyer. The city also offers a program, but it's got quite a few strings attached - but if you're low income it's worth looking into.
Here's a state resource: http://first-time-home-buyer-s.com/first_time_home_buyer_gra
Here's a city resource: http://www.nyc.gov/html/hpd/html/buyers/downpayment.shtml
Take a good state-approved class in buyer education, and consider HDFCs, which are cheaper and need less money down. Visit the Urban Homesteading Assistance Board site for more.