This is basically stating that you've reached the max connections allowed to MySQL. Are you on a shared server or is this your own server? If it's your own/dedicated server then it's just a matter of bumping up max_connections if the server has the resources.
If you're on a shared host, then it's a bit tricky. The error message is the global one, meaning that they have a set amount of connections for all domains on the machine, and it's being reached, and they might not bump it.
