That's the immobilizer chip. It's a little pill-shaped RFID-like thing that's been inside keys since long before remote locks and push-to-start. Basically any key that has some plastic instead of being entirely metal. The reader is located immediately next to the ignition key hole on the steering column, and that location is sometimes used even in push-to-start cars although apparently in your case it was near the start button instead. Distance is limited to a couple centimeters max. Car won't start unless the immobilizer's reader sees the correct key. When a push-to-start fob's battery is in working order, the distance is moot because it uses full blown RF instead.