I’m not sure what others see as the context of the meme, but in my experience it’s normally when you are fiddling with it, but you never expect it to be the problem because it seems so simple.

There are many reasons you might need to fiddle with is. The most obvious is when you move your server to a new computer, it might get a new IP address. But your browser might cache the old address. Your computer might cache it. Your DNS server might cache it (like the rest of the internet, there is not one big DNS server but many smaller ones - most non-technical people would be using one provided by their internet provider). It might not be working and you presume it’s a problem with the new server but actually it’s the DNS.

But also DNS as a system is also used for things that are not directly related to looking up a domain name. For example, when sending an email, there are many checks on the receiving side to ensure that the email is actually coming from somewhere that is allowed to send an email from that domain name. I can send an email to you from bill@microsoft.com, but it would go straight to spam because it would fail those checks. DNS records are used to authorise servers that can send email on behalf of that domain. And just generally DNS is used for proving domain ownership (for example, it’s one method to get a certificate from Let’s Encrypt to allow secure connections to your website).