My website has member side and after adding a member to a site the site was broken and for members, Initialization Error occurs. so members couldn't access their own page on the website. and also when I install the new plugin I get this error again. I couldn't change anything on the website because after adding new page or post I have this problem. What is the reason of this problem?
Your screenshot definitely points that your MySQL connection is not correct that is defined in civicrm.settings.php file.
You can use MySQL Workbench to test the database connection or if you have access to phpmyadmin you can test it through there too.