iOS Settings – What Does ‘Learn from this App’ Mean in Siri & Search?

It appears that very little, and it can be completely disabled.

Carrier IQ, the now infamous “rootkit” or “keylogger”, is not just for Android, Symbian, BlackBerry, and even webOS. In fact, up through and including iOS 5, Apple has included a copy of Carrier IQ on the iPhone. However, it does appears to be disabled along with diagnostics enabled on iOS 5; older versions may send back information in more cases. Because of that, if you want to disable Carrier IQ on your iOS 5 device, turning off “Diagnostics and Usage” in Settings appears to be enough.

http://blog.chpwn.com/post/13572216737

Upon a little testing around, I have discovered the solution. Go to Settings > General > Spotlight Search and disable Bing Web Results. There must be some problem either on Microsoft's end or in the way the iOS software gets it, and this interferes with Spotlight from doing what it needs to do.

Hopefully Apple will fix this and it can be re-enabled with iOS 10 or a future iOS 9.x update, or it will be fixed on Microsoft's end, if the issue becomes known to them.

It's unclear to me if this affects everyone or just a small number of users. If you're not sure if you have this problem, test it out as per the original question. And please comment if this does or does not fix it for you.