I'd say contact your host. There's too many people trying to connect to the server and I don't think there's anything you can do to fix it.
Essentially, your forums are far too busy for the amount of connections your host provides.
Only a certain amount of people can access your website at any one time. If it goes over this limit, you'll see that error. MyBB can limit the amount of people that can access it when it reaches a certain server load, but I'm not too sure about connections...
Talk to your host, and see if they will increase the max_user_connections number. If not, there isn't much you can do besides changing hosts.
Looks like you have quite a huge and active forum. I suggest switching hosts or upgrading your plan if available; if the problem persists.
Best Regards.