'mysql' database in fresh MySQL installation
The mysql.servers table is used only in conjunction with any table that uses the FEDERATED Storage Engine. It's in the MySQL Documentation:


  FEDERATED tables may be replicated to other slaves, but you must ensure that the slave servers are able to use the user/password combination that is defined in the CONNECTION string (or the row in the mysql.servers table) to connect to the remote server.


Therefore, a freshly installed MySQL instance will have mysql.servers empty. If you create a FEDERATED table, then the username/password for a remote table is populated in mysql.servers.

What you are looking for is the information_schema database. For example, 


INFORMATION_SCHEMA.SCHEMATA has all the databases in the MySQL Instance
INFORMATION_SCHEMA.TABLES has all the tables in the MySQL Instance
Please Read the Following


MySQL Documentation on INFORMATION_SCHEMA
My 4-Year-Old Post How is INFORMATION_SCHEMA implemented in MySQL?