Because changing your nameservers to cloudflare's allows you to use their DNS service, which comes with the CDN infrastructure.
Here is the cloudflare dns for my lemmy server's domain:
The switch where it says proxied means that I am using the CDN to obfuscate the real IP of the server.
Pretty much yes.
If you want a more in-depth explanation of DNS and how nameservers work etc check out this article from cloudflare.
Specifically the part; "There are 4 DNS servers involved in loading a webpage:" It explains it much better than me.