There are a several reasons that you may want to modify a standard report and save it as a new report:
You may want to add a report or report link dashpart. You cannot add standard reports as report or report link dashparts.
Report options are only remembered for the current session. If you run a report on a regular basis and you don't want to keep setting the options and criteria every time you run it, you can save it as a new report.
You may want to share the modified report with others.
Click 
in the Report grid Options column to display the Report Options dialog
box which allows you to edit the report name, select the columns that
display on the report, adjust the page settings such as margins and orientation,
and set default number, currency, and date formats, among other things.
When you modify standard report options, you can save them for future use. If you save them to the Personal Options folder, then only you as the report owner can use them. If you save them to the Global Options folder, then all users with access to that report can use them.
The Report Options dialog box is not available for all reports and the available tabs and options vary depending on the type of report selected.
Report criteria define the filter that the system should use when creating the report. After you specify criteria, you can save them to a Personal Searches folder, or you can save them to a Global Searches folder if you want others to have access to them.
Click 
in the Report grid Selection
column to display the Search dialog box that you can use to define the
filter.
See Specifying Criteria vs. Specific Records (Values) for information about the difference between selecting report search criteria vs. records (values).
By default, a new report saves as a personal report. No other user can view this report (even as a report dashpart) unless you use Access Control to grant other users access.
Modify options for a standard report
Save a modified standard report as a new report
Share a modified report with other users