/Applications/iOS Diagnostics.app

This hidden app was introduced in iOS 4.1. When run, the user is prompted for a ticket number.

It has links to iosdiags.apple.com, which you can go to. It also seemingly submits logs to Apple through https://iosdiags.apple.com/MR3Server/MR3Post. It also has references to "Mobile BehaviorScan" and utilizes the diags:// URL schema. Adding a number to the end (i.e.- diags://1) causes it to show an agreement.

Its principal class is MobileBehaviorScanAppDelegate.

Localization strings

Extracting its English localization strings yields these:

/* Privacy Information */
"By clicking “Send to Apple” you agree that Apple may periodically collect diagnostic data from this device, including the device serial number, device name and daily count of call attempts. This data will be used to troubleshoot issues with your device and to improve our products and services. For information on Apple’s Privacy Policy, see <a href=\"http://www.apple.com/legal/privacy\">http://www.apple.com/legal/privacy</a>." = "By clicking “Send to Apple” you agree that Apple may periodically collect diagnostic data from this device, including the device serial number, device name and daily count of call attempts. This data will be used to troubleshoot issues with your device and to improve our products and services. For information on Apple’s Privacy Policy, see <a href=\"http://www.apple.com/legal/privacy\">http://www.apple.com/legal/privacy</a>.";

/* Cancel */
"Cancel" = "Cancel";

/* Done */
"Done" = "Done";

/* App Title */
"iOS Diagnostics" = "iOS Diagnostics";

/* Last Sent: */
"Last Sent:" = "Last Sent:";

/* Never */
"Never" = "Never";

/* Next */
"Next" = "Next";

/* OK */
"OK" = "OK";

/* Send to Apple */
"Send to Apple" = "Send to Apple";

/* Sending to Apple... */
"Sending to Apple..." = "Sending to Apple...";

/* Ticket number is not valid error message */
"The ticket number was not found. Verify the number and try again." = "The ticket number was not found. Verify the number and try again.";

/* Submission error message */
"There was an issue with your submission. Please make sure you are connected to the internet and try again." = "There was an issue with your submission. Please make sure you are connected to the internet and try again.";

/* Ticket Number Placeholder */
"Ticket Number" = "Ticket Number";

/* Ticket Number: */
"Ticket Number:" = "Ticket Number:";

/* Ticket validation server is unavailable error message */
"Ticket validation has failed. Please make sure you are connected to the internet and try again." = "Ticket validation has failed. Please make sure you are connected to the internet and try again.";

/* Enter Ticket Number */
"To receive support services, enter the ticket number you were given." = "To receive support services, enter the ticket number you were given.";

/* Submission success message */
"Your information has been received by Apple." = "Your information has been received by Apple.";

Based on these strings, it appears to be something like CrashReporter on the Mac, allowing you to submit logs to Apple on-the-go. Interestingly, ticket numbers are used, implying someone at Apple would respond to you regarding the issue.

Reference

Analysis on MacRumors forums