An instance number enables you to select which instance of LiveZilla (auto-)connects to which server.
This is required when you want to connect to multiple LiveZilla servers at the same time (using multiple instances of the LiveZilla Operator Client).
You run two different websites and you want to be connected to both of them at the same time. Set instance number 1 for your first server and instance number 2 for the second one. When starting the Operator Client of LiveZilla twice the first instance will now connect to your first server, the second instance will connect to the server profile with instance number 2.