NFC stands for Near Field Communication. It is a very short distance radio signal that would allow you to you use your phone as a credit/debit card; just like the Japanese and some Europeans have been doing for almost 10 years.
There are rumors that Apple will be including this capability in the next version of the iPhone. I have not heard of any inclusion in future models of competing phones.
What this will allow you to do is let your wireless phone carrier (AT&T-Mobile, Verizon or Sprint) manage your day-to-day finances for you. For a suitable charge, of course.
Will this actually happen? Who knows? This capability has been talked about since the days of dial-up modems and Palm Pilots, so it may yet be a ways off.
If it does come about, you should be wary of your mobile phone provider giving you short term loans that you promise to pay off when the cell phone bill comes.