The Android app is made using MIT App Inventor which is an easy way to make Android apps.
The Arduino is connected to the Android device using OTG cable, the device also powers the Arduino. The communication is transferred in serial protocol. The app has buttons to connect and disconnect the USB to the phone. There are also 3 LEDS that indicate the Arduino inputs state and 4 tick boxes to control the outputs of the Arduino.
The .apk file is the file that installs manually the app to your device. If you wish to change the app the .aia file can be imported after you install the MIT App Inventor. You can download the app from github.
When you start the app it tell about an error of the USB not connected, sellect to connect to the USB and restart the app.