In most cases, NFC tags are stickers – they can be visible to you, or also be placed for example on the back side of a poster.
The NFC tag contains a little chip and an antenna. The chip stores the data and takes care of communicating with the reader device – e.g., your NFC smartphone. Your smartphone also contains an extra antenna used for NFC.
If you tap a tag, your phone and the tag communicate with each other. The antenna is used to transmit data and energy between the rader and the tag. It allows your phone to read the tag; if it’s a re-writeable tag, the device can also store data to the tag.
The tag doesn’t contain a battery; it’s powered by the electromagnetic field of your phone.