You can use anayltics for all kinds of things. You can record times like i did in order to see the performance of your software. then in slow parts you can run a time profiler if you are using xcode. What a time profiler does is it will tell you all the calls that were made and how long each one took so the developer can pinpoint the slowness. For websites you can use it to see how often was your site down, how many people are visiting, where are they from, how long were they on the site, what OS were they using. There is so many applications for analytics.
So besides performance what other things can QA learn. Well you can learn what OS and browser they were using so you know what to test more then another scenario. You can learn what is happening in the field rather then a controlled environment and you can try to recreate it with all the given information. This can help you get ahead of the game.
Here is a QA Gif for you: