The index.php contains two buttons, an "on" and "off" button. Let's walk through the scenario where the user clicks the "on" button.
Once a user clicks "on," index.php writes {"light": "on"} in light.json.
The ESP8266 connects to wifi and pings light.json. In this case, it reads {"light": "on"}. So it turns it's GPIO2 on HIGH.
The ESP8266's GPIO2 on HIGH turns the LED on. The LED is just a visual signal to let you know it's working. IT'S WORKING!
The ESP8266's GPIO2 on HIGH also connects to the ATtiny85's GPIO4. When the ATtiny85's GPIO4 reads HIGH, it sends um, signals to the motor driver. Which motor driver, you ask?
THIS MOTOR DRIVER!!!! The L293D motor driver, which through.. um, signals, turns on the 5VDC Stepper motor.
.. and the stepper motor turns. Spin spin spin!
Oh right, power. This whole thing is powered by a 9V battery. But there's one problem. The ESP8266 takes 3.3V and the ATtiny85 takes 5V. hmmm...
REGULATORS! Here's one that converts voltage to 3.3V. It gives the right power to the ESP8266 and the LED.
And here's one that converts voltage to 5V, which powers the ATtiny85 and the L293D Motor Driver. And there's the set up. That's all folks!