Is that a capacitor and how does it work?
Yes, the zigzags are to match the RFID antenna. 

The basic idea is that the impedance of the antenna and the impedance of the whatever you are hooking the antenna up to need to be matched in order to transfer power from the antenna into the input circuit. 

Whoever designed this probably used a simulator to figure out how to make those zigzags and then measured the results on a vector network analyzer.

Read RF Circuit Design by Chris Bowick to really understand (and then get some play time on a network analyzer).