NFC stands for Near Field Communication. It is used to share data or pay using your phone by just tapping it to another device. This is completely off topic but i am feeling just like i am answering in school. You can enable android beam and send a small amount of data(images, videos or contacts) by just touching the phone together. Go to the thing you want to share, click on share button and select ANDROID BEAM. Now touch two phones together on their back while NFC is enabled.
As rightly explained by @DuonicGamer, NFC is like bluetooth but with a shorter range. So NFC is used to connect wireless headsets, if the two phones have NFC, you can transfer data and then, it is prominently used for payments as well like samsung pay.
