My father recently brought home an old identification card, and after cracking it open I found that it consisted of simply a large coil of wire, connected to a small electronic chip (which was so small that I sadly lost it - it looked something like this but a lot smaller. Incidentally, it was so small that when I was cracking open the ID tag it actually got a bit damaged).
It works as an identification card, in that when you swipe it close to a detector, it registers your identity. I could (and have) made some guesses as to how it works (probably involving a magnetic field?) but many times my guesses turn out to be wrong, and I can't seem to be able to find a good physical explanation online as to how these identification cards function, and how they store your identity.