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There are two sides of censorship-resistance that are important when it comes to DNS. Censorship-resistance/seizure-resistance for owners and censorship-resistance for consumers.

For owners, it's important that their domain names can't be taken down or seized from them. Sci-Hub has dealt with this issue numerous times and has had to register a pool of domain names to try too counteract this issue before getting their Handshake name. Domain registrars can seize domain names and there isn't much recourse for the owners — it doesn't even need to be for a good reason[1]. On Handshake, ownership is controlled by your wallet's private key (similar to owning Bitcoin). As long as you control your private key no one can take your name from you.

For consumers, it's important that you can 1) access the domain name and 2) trust that the DNS records you're seeing are authentic. Handshake is a distributed network so as long as you can connect to a single node you can access it. This mechanic is what gives other distributed networks like Bitcoin and BitTorrent their strength. Furthermore, you can verify the authenticity of the records since each DNS update is reflected on the blockchain similar to how you can verify transactions on Bitcoin.

[1] https://www.izoologic.com/2018/12/20/zoho-domain-taken-mista...