NFC products send signals to each other using a principle called "resonant inductive coupling". A metal coil with an oscillating electric current passing through it will transfer energy to another nearby metal coil. If you take apart an NFC smartphone or NFC tag, you can see these metal coils. By passing energy from one coil to another, NFC smartphones and tags are able to "talk" to each other.
NFC can only communicate at very short distances. This is different from Bluetooth, Wi-Fi, and other radio devices which can transmit signals at longer distances. NFC is based off of the same standard used by smartcards for mass transit systems around the world. In this standard (ISO/IEC 14443) the communication distance reaches up to 10cm. Although, typical distances are up to 3cm.
About NFC Tags
You can find NFC tags made into stickers, wristbands, keychains, cards, and more. However, they all have two things that make them work: an antenna and an NFC chip.