The "too many connections" error occurs when a MySQL server reaches its maximum allowed number of client connections, causing the server to return an error message. This error is often caused by high-traffic applications or unoptimized applications that do not close connections properly. To resolve this issue, one can increase the value of the max_connections variable temporarily or permanently, and also follow best practices for MySQL configuration such as monitoring connections, optimizing applications, adjusting max_connections, configuring wait_timeout, implementing connection pooling, regularly reviewing configuration, and considering scaling. Additionally, increasing the default connection limit set by MySQL may be necessary for high-traffic applications, and sudden traffic spikes can lead to connection errors.