Cloudflare is something that sits between you and the websites that went down. For example if you trying to access reddit.com and Reddit uses Cloudflare, if you try to go to reddit.com in your browser, your browser will be taken to Cloudflare instead. There they will check whether you are a bot or not (other things are done as well though I am not sure), and if they like you they will serve you the website.

If Reddit is using Cloudflare, they have to configure their DNS to send you to Cloudflare. This means you cannot view Reddit without having to deal with Cloudflare. So if Cloudflare goes down for some reason, it means you cannot access Reddit.