The error message
Error No. 2005: Unknown MySQL server host 'some_URL_or_ip'
simply means that connection is not possible for the following (or similar) reasons:
A protocol is specified in the "MySQL host address" field of the SQLyog Connection Manager that does not support MySQL connection. It is a common mistake among beginners to use "http://...". Don't! Just "www.myveryowndomain.com" or "sales.myowncompany.biz" or "localhost" (if the webserver and the MySQL server is running on the same computer). When connecting to a remote network you may need to ask the Sys Admin there for the correct URL to use for addressing the MySQL server.
However if you use HTTP-tunneling the URL-field on the Tunnel -tab of the SQLyog Connection Manager should be a complete URL with the "http://" protocol specified. This is because the tunneling script must be addressed through a webserver (that is the idea of HTTP-tunneling!).