Varnish debugging involves gathering data from tools like varnishgather, varnishlog, and varnishtop to diagnose different types of issues like stability problems, functional bugs, operational performance issues, and capacity limitations. The document provides examples of how to use these tools to debug crashes, trace code execution, examine request headers, monitor hit rates and response times, and analyze backend communication. It emphasizes that debugging requires understanding the problem being experienced and leveraging tools like varnishlog to obtain request details, error codes, and timing information.