AirParrot Remote does not enable mirroring from the mobile device. It is used as a remote control for AirParrot 3 on your computer. This means that your mobile device using the AirParrot Remote app can control AirParrot 3 and mirror your computer screen from the app, without needing to be near the actual computer that you will be mirroring.
AirParrot Remote will also allow you to remotely control the computer while mirroring. One example of this would be using AirParrot Remote to run a presentation from a computer that has AirParrot 3 installed. In this case, you could run the presentation from your mobile device using AirParrot Remote, with no need to touch the computer doing the presenting!