Well, without knowing exactly which batter you got, it's pretty hard to know if it's a non-NFC one or not. If you don't know what the feature is used for, chances are you won't need it anyway, but you could be missing out on a few cool features.
NFC stands for Near Field Communications. That means that something communicates with something else, and that the communication takes place when the two devices are in close proximity. OK, now that the 'technical stuff' is out of the way, to the 'goodies'.
With NFC you can do a few cool things. For instance, if you have two phones with NFC and you activate the sharing feature (some phones call it Android Beam, some S-Share, some NFC Sharing, etc.), it will automagically start the transfer between two devices when you put them together, usually back to back. If your looking at a picture, for instance, just tap the back to another compatible phone and voilá, you'll hear a beep, you can separate the devices, and the system will do the rest.
But perhaps the one feature most people are trying to use these days are payments using your phone. With that NFC chip you can initiate payments using apps like Android Pay or some bank-specific apps (again, for this to work you'd need an NFC-compatible terminal, and while those are rising in availability, they're nowhere near as ubiquitous as magnetic strip readers, which is why Samsung's new phones have that advantage since Samsung Pay also works with normal terminals, but that's another story and one that, sadly, your Note 4 doesn't support).
Some hotels are also starting to offer to 'code' your room key into your phone so that you can open it with the NFC chip. Just tap the back of your phone to the door reader, and it opens (provided it is your room and/or you're still paying for it).