What does "WARNING: [pool web] server reached max_children setting (2), consider raising it" mean?

I keep seeing this in my site logs. Does this mean my site is down? How do I raise the max_children setting?

WARNING: [pool web] server reached max_children setting means your service has reached the maximum number of PHP children processes. This is caused by too many PHP requests to the service or by long running/stuck PHP requests. This may also result in 503 errors in your web application.

Please read through our PHP-FPM documentation to explain the issue in more detail. This documentation also provides a way to check your applications memory usage and adjust the max_children allocation.