I'm very confused.

I basically understand how DNS works. Here's an example that helps illustrate what I'm having trouble understanding.

Right now, I run a small web-server. I use my provider's DNS manager, so I don't have a DNS server hosted on the machine.

Let's say for a second, that I don't use my host's DNS, and I decide to set up a DNS server on my server. Hypothetical scenario: my server (entire) server goes down - DNS included. Why do I need backup DNS? If the server is down, who cares if the DNS server is down too, considering that even if I had DNS up (it wasn't on the crashed server), it wouldn't be able to forward requests anyway since the server would be down?

Is the point of having secondary DNS, to be able to change the IP addresses that your DNS server points to, so if your webserver was down, you could redirect traffic to a backup? How would you switch to the secondary provider, in the event that your main DNS provider becomes unavailable? Is a backup DNS system basically up all the time? How is it configured? Is it just an exact clone of the DNS server you would have on your server? Do they run simultaneously?

Hopefully someone can see what I'm hung up on, and provide some guidance. Thanks