What is it? How does it work? How it can be helpful?
Power BI quickly searches different subsets of your dataset while applying a set of sophisticated algorithms to discover potentially-interesting insights. Power BI scans as much of a dataset as possible in an allotted amount of time. You can run Quick Insights against a dataset or tile (Related Insights). You can readily use any of suggested visualizations (i.e. quick insights) and build Report or Dashboard in minutes 🙂

So, in short – You can build your Report or Dashboard quickly by browsing through Dataset’s data insights. Then choose whatever insight (visualization) you think is appropriate for your case and add to your Dashboard. Later, you can customize if you need.

How many types of “Insights” are available?
As of now, we have 9 quick insights available for us. Power BI runs some smart algorithms to get insights out of your Dataset and present into easy to understand format (visualization).

1. Category outliers (top/bottom)
   Highlights cases where, for a measure in the model, one or two members of a dimension have much larger values than other members of the dimension.
2. Change points in a time series
   Highlights when there are significant changes in trends in a time series of data.
3. Correlation
   Detects cases where multiple measures show a correlation between each other when plotted against a dimension in the dataset.
4. Low Variance
5. Majority (Major factors)
   Finds cases where a majority of a total value can be attributed to a single factor when broken down by another dimension.
6. Overall trends in time series
   Detects upward or downward trends in time series data.
7. Seasonality in time series
   Finds periodic patterns in time series data, such as weekly, monthly, or yearly seasonality.
8. Steady share
   Highlights cases where there is a parent-child correlation between the shares of a child value in relation to the overall value of the parent across a continuous variable.
9. Time series outliers
   For data across a time series, detects when there are specific dates or times with values significantly different than the other date/time values.

Please see this link for each algorithm’s sample visualization for better understanding:
https://powerbi.microsoft.com/en-us/documentation/powerbi-service-auto-insights-types/

Can I customize that?
Yes, you can choose the insights you like. Add that into your Report/Dashboard. Select the visual and change its properties as you like.

How do I improve my “Quick Insights”?
First of all, you should be a “Dataset Owner”. Because quick insights are all depends on your data available in Dataset. So, if data in Dataset is not statistically significant then Power BI may not be able to produce all quick insights (visualizations) for you.

But few quick tips that you can try are here:
https://powerbi.microsoft.com/en-us/documentation/powerbi-service-auto-insights-optimize/

Thanks, Khilit