When creating a privilege, what happens with underscores in the database name ?

If you do not put a backslash before the underscore, this is a wildcard grant, and the underscore means "any character". So, if the database name is "john_db", the user would get rights to john1db, john2db ...

If you put a backslash before the underscore, it means that the database name will have a real underscore.