I am working with a report that contains the objects:  Connections, Occurrences, and Opportunities, where Connections is the most detailed information.  Note the field that I have in the report.

Do you remember how easy it was to add columns to a report?  Summarizing uses the same drag and drop method.  If you want to summarize by a field, you grab it and drop in the drop zone.  In this case, I am going to grab the Field Header of Contact and drop it in the Drop Zone.  Note that the Green Check Box appears when I am in the Drop zone.  Release your mouse.

The blue bar shows that we are summarizing by the field Contact (from the Connections Object).  The details show the Start and Date time of the Occurrences, and the Name of the Opportunity.  Also note that a record count has been included in the Summary.  The count is of the most detailed information... in this case, it would be Occurrences, and not Opportunities

If I am not interested in seeing the Details, I can always hide them by un-checking the box.  REMEMBER:  I am currently in the Customize Report Window and the Preview only shows me a portion of my records... if I wanted to see them all.  I could run the report at this point.

Let's add another summary under each Contact of the Opportunity.  You see, we have another drop zone which allows us to summarize further.  Grab the Opportunity name and drop it here.  When you have dragged the field to the right place, the drop box turns blue, and the Green Check Box appears for the field.

Salesforce has an extensive knowledge base for Reports and Reporting Summaries in their Help and Training Section.

For more information see:  Salesforce Help and Training: Summaries