Connect failed: Too many connections

My site and pages were working perfectly yesterday and before but not anymore, while I haven’t changed anything since last night (when everything was still working). I just turned on my computer, went to my site and the index page is working fine but when you click on a link (ie: about) it gives me a white page with the text:

Connect failed: Too many connections

Does anyone know what this means and what I can do to fix this? I’m quite new to WP so this is the first time I got this error. It’s so strange that the site stopped working while I was sleeping.