For the most part, you can't have a web site that uses encrypted communication (https:// as opposed to plain old http://) without buying (renting really) and using a domain name. The domain name is what they are calling the "DNS dependency".
So for a nym like me, it is very difficult to host a web site anonymously. In the old days, I just had to get an ip address and do something like http://12.34.56.78 Now I have to also rent a domain name from some permissioned authority.
And it isn't just about trying to do all this anonymously, the fact is, these are all points of control over the internet. The system is run by people and companies that have to obey laws, so my web site could get taken down if the powers that be want to take it down.
With #nostr, I don't have to get permission and rent an ip address, I don't have to get permission and rent a domain name, I can just create my own npub without permission or paying anybody, and I can make as many npubs as I want.
If we can make #nostr the base layer of the internet, we solve these fundamental design flaws in the internet that were made when we didn't know any better.