If you are seeing an Error 523, it means that there is an issue from the origin web server, as it's unreachable.
A common cause is that the DNS setting has changed. Sometimes, hosting providers update the origin IP information for their customers. If this is the case, you need to make sure the new origin IP address for your A record is reflected in your CloudFlare DNS Settings page. Once make the change in your CloudFlare DNS Settings page, wait up to 5 minutes for it to take effect.
Another common cause of 523 errors are internet routing issues between CloudFlare's systems and the origin (i.e. the web server where the site is hosted). This can be caused by issues with an internet provider between your origin and CloudFlare, or with the origin itself. If you are confident this isn't caused by your web hosts, a useful piece of information to give to CloudFlare's support team is a traceroute between your origin and one of CloudFlare's IP addresses (ideally one of the addresses that you usually see send requests to your site). You can find instructions on running a traceroute test here. That should help them to pinpoint the issue.
523 errors can also be caused by Railgun. If you are the customer of a Hosting Partner of CloudFlare and you are using their Railgun, you should contact them about this. If you are running your own Railgun, then you should contact CloudFlare's support team, providing the most recent syslog file from your Railgun server if that's possible.