Application Insights is an extensible analytics service that monitors your live application. It helps you detect and diagnose performance issues, and understand what users actually do with your app. It's designed for developers, to help you continuously improve the performance and usability of your app. Simply, you install a small SDK in your application, and set up an account in the Application Insights portal. The SDK monitors your app and sends telemetry data to the portal. The portal shows you statistical charts and provides powerful search tools to help you diagnose any problems. For more info, you can refer: https://azure.microsoft.com/en-us/documentation/articles/app-insights-overview/
In order to learn more on this, I will suggest you to have a quick look at this video; you will learn advanced querying concepts with Analytics. It provides an overview of the telemetry data that Application Insights collect and how you can you use interactive querying to get instant answers to your questions.
Hope this helps.