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There are many RFID (Radio Frequency Identification) labels available, so I'm showing this one for illustrative purposes.
Most labels are actually either adhered over the barcode on products or are built into the packaging (as for pillows they're put on the pillow's tag, not into the pillow).
If you look at the bottom of that image, you'll see a very thin wavy wire. That's the antenna. In the middle of that antenna is a very small chip. This chip holds a very small amount of data. Typically, it's the DPCI, a short product description (name, color, size, department...) and maybe the UPC. Because of the chip size, it's not a lot of information. These chips are non-powered.
The RFID Gun (or wand) produces a radio frequency. This frequency is picked up by the label's antenna and activates the chip. The chip then send a response signal, which is a string of data, that the RFID wand picks up and matches to the data it's looking for. The more the data matches, the stronger the response. You know you're in the right area when you see the LED on the back of your RFID gun flashing. That's the first indicator you're "close to similar items". This typically means the data is starting to match, you're looking in the right department (you're in shoes, looking for shoes for example). The more data matches, the RFID gun will begin to chirp louder and/or the bar indicator on your Zebra MyDevice will grow more solid.
Obstructions, such as stacked product, shelving, boxes and walls will weaken the signal and you'll get a muddled response. But, if you see any response, you know the item you're looking for is nearby.
In summary:
Labels have a non-powered ID chip connected to an antenna.
Gun sends out radio frequency request that activates these non-powered ID chips.
Chips respond if requested data matches. The more the data matches the request, the stronger the response. (Louder chirping noise and fuller bar indicator)