The scholarly conversation is the process of scholars and researchers in a particular field publishing their own work, suggesting areas of further research, and responding to the works of others.
For example, when you read a scholarly article, you'll notice that there are usually quite a number of citations. This is how an author acknowledges and responds to the works of others. They are drawing from and utilizing those other works and "responding" to all or part of what previous researchers have produced. At the end of their own article, they often acknowledge shortcomings in their own research, and suggest areas where further studies are needed to fill in the gaps. Down the line, you may see another scholarly article be published that then cites the first article, picking up the thread of the "conversation" where the previous researcher left it. They may then continue that same conversation, or utilize that research to branch off in new directions.
Conversations such as these, happening between researchers all sorts of fields, are traced through their citations. By following citations and "conversations" between researchers over time, you can see how scholarship in a particular field has developed and evolved.