The "app" that gets installed is actually a webclip, not a native iOS application. They embedded the icon as a base64 string inside the .mobileconfig.
The webclip opens mobile Safari in fullscreen, with a link in the format of "http://mocava.de/ios/parental-control/profiles/UNIQUE_ID/par..., where UNIQUE_ID ties back to the choices you made on the setup screen of their website. This will allow Mocava to track usage stats, which seems like a fair trade-off for a free service.
You could roll your own version of this using Apple's Configurator application, however Mocava has done a decent job of streamlining the setup and installation.
Thanks :) Usability wise, the hardest part was to explain that you have to install a profile to deactivate an existing profile. Also people associated the word "profile" with a facebook profile and thought it contains their personal data like name & address. To prevent confusion, the page I removed (almost) all instances of the word profile from the page.
One nitpick. It is confusing that all your options are named "disable" and "allow" but your instructions say "if you set this control, it will disable...". So the control is "set" when it says "disabled"? It is also against convention in the sense that your options are negative-positive (disable-allow) when the convention is positive-negative (yes-no, set-unset, block-unblock, etc).
Personally, I would change the controls to "block" and "unblock", and the instructions to something like "set this to block to disable and hide... ". In the very least, I would change them to "enable" and "disable", in that order.
Edit: just wanted to add that after completing the whole sign-up, I found your overall style clear, concise and organic. You did get a lot of things "just right". Great job.
And one last nitpick/question. It looks like the app requires a connection? Was it simply easier to develop, or did you want to simplify the sign up process by tying users' settings to their email? It would obviously be much better if this worked in Airplane mode. However, it's not a dealbreaker, and the unusually low friction of getting set up may be worth it (in fact, if that were the goal, I think it's kinda genius).
groups.google.com/group/hn-parents
I vaguely recall there being a discussion on it a while ago about this.