The button reads "auto" and there are two LED lights next to it. When I press the auto button the left one turns on.
Also on the opposite side of that mirror there's this thing that looks like a camera or senor of some kind. What is that for?

 

It's to turn the auto-dimming mirror on and off.

The LED just tells you it is on (auto). The sensor at the other end is to detect bright lights behind the car. There is also a sensor on the other side of the mirror which detects the ambient light level.

If it is dark and you have a car behind you the mirror will dim. You can test it by turning it to auto, covering the sensor on the rear of the mirror and shining a light at the sensor next to the auto button. You'll see it dims slightly, not much but it is enough to protect your sight!

 

The other sensor is the rain sensor and it controls the speed of the wipers during rain.

Salim

 

In the photo that's the black unit stuck to the screen to the right of the mirror.