Quick Insights is a way to summarize data quickly to gain insights.  It uses the approaches available in Insight, but makes them available directly from the dataset in Data Manager.  After selecting a dataset in Data Manager, select the Quick Insights link:

You can select any of the available Insight types, such as Chart, Table, or Pivot.

After selection, you will be provided with options similar to those provided in the Insight area of LityxIQ.  With Quick Insights, you will not have the option to save the Insight as you do in the Insight area.  Quick Insights are an option for doing on-the-fly analysis of your datasets in an informal fashion.  For a more formal analysis that can be saved (and for example, be placed into dashboards), you will need to use Insight.