The Search tool in Application Insights is useful for quickly querying data, but it's not suitable for complex searches where you try to find correlations between different events, nor for visualizing your data.

The Analytics web tool is a more advanced query and visualization system, through which you can inspect the data that Application Insights collects. Click on the Analytics button in the Application Insights search blade: 

The Analytics web tool will open with a default query to search all the events that happened in the last 24 hours:

The query language that is used in Azure Log Analytics is very rich and can only be used to control the rendering of results. For example, this query will show a time chart with the requests duration percentiles for the last 12 hours:

requests
   | where timestamp > ago(12h)
   | summarize percentiles(duration, 50, 90, 95) by bin(timestamp, 1m)
   | render timechart

Azure Log Analytics is a complex system with many features. To read more about it and learn how to use it, check out the Getting started guide at: https://docs.loganalytics.io/docs/Learn/Getting-Started.