MySQL error codes are used to communicate errors between the client and server. Each error includes an error number, SQLSTATE value, and error message. Common MySQL error codes include 1040 (too many connections), 1045 (access denied), and 1064 (syntax error). To fix these errors, one can increase the max_connections variable for connection usage, reset passwords, or proofread code for syntax issues. Non-coded errors such as packet too large, can't create/write file, commands out of sync, hostname is blocked, and aborted connections also occur and require fixes like increasing packet size limits, specifying temporary directories, checking function orders, modifying hostname block settings, and reviewing error logs. Understanding how to handle these errors can help developers troubleshoot and resolve issues efficiently.