The Drill Down picklist and button allow users to report and filter Reports on the fly right from the Run Report page without clicking the Customize button.
If you aware, when running a Matrix or Summary report, there will be checkbox for each group.
At the bottom of the report, there is drill down picklist and button.
Select checkbox (for this example: Opportunity Owner) then select a value to drill down (example: Industry from Account object) and click Drill Down button. It will run the report with filtered by the Opportunity Owner and group by Industry.
If you save the report, the filter and group will become permanently save.
For Matrix report, you will find 2 "Summarize information by:" at the report option. The left one would be for row group and the right one for column group. You can change this value on the fly without customize the report.
While for Summary report only have 1 "Summarize information by:" for the first grouping.
On top of Show and Time Frame, for some standard object, such as Opportunity, you will find Opportunity Status and Probability option.
While for Case, we will have Units option.
Reference: The Report Run Page