What are A and A* conference ranks?
In computer science, the most important ranking is the one maintained by CORE, the Computing Research and Education Association of Australasia. It uses ranks such as A* (=exceptional), A (=excellent), B (=good to very good), and C (=sound and satisfactory).

They make the criteria for the different ranks explicit in a formal ranking description document.

Also, they have an online database with their rankings.