Right now it's only available in JetBlue's Terminal 5 at JFK. More info over on JetBlue's blog. Their website is here.
UPDATE Feb 2016: sadly this service has been discontinued. I thought it was really useful, maybe it can come back in a different form someday...
The kiosk is right after you clear security. It opens at 5am and closes around midnight, but the staff let me know that they monitor inbound flights and will stay open later in the event of delayed flights.
It's all run from a tablet – just put in your phone number, it takes your picture, you swipe your card, tell them when you'll be back, and you're off. When you get back, you punch in your phone number, your face appears onscreen, and the attendant gives you back your coat. All receipts are automatically sent to your phone as a text message. The fee is $2/day. Simple and super convenient.