The report_methodology command reports
additional constraints and timing analysis issues, which you must carefully review
before and after running the place and route tools. This section describes the main XDC
and TIMING categories of checks, along with their relative impact on timing closure and
hardware stability. You must focus on resolving the checks that impact timing closure
first.
See this link in Vivado Design Suite User Guide: Design Analysis and Closure Techniques (UG906) for more information on some of the following checks.
Also, see the Adoption Of The Methodology Report blog
series to get an understanding on how report_methodology helps resolves issues and saves you time.