Hello Bally,
Just a quick introduction about me - I've 4 years of experience as a Web developer. I don't only code but I teach coding ( JQuery, PHP, MySQL, Wordpress etc) to others on my popular blog http://youhack.me.
Are you getting this error randomly? If yes, then I bet you are using a shared hosting. It seems that when Wordpress is connecting to the database, it is timing out. If you're getting this error permanently, then the database username and password is wrong or not correctly assigned. Either way, let me know I'm available to investigate into this issue for you right now.
Looking forward to work with you on this small task.
Regards,
Hyder