I'll give you a quick, very high-level, run down.
1) All domain names on the Internet are provided by registries.
2) Those registrars control your domain name, because THEY tell the Internet which name servers to use to resolve names.
3) Those registrars can be ordered, by their respective governments, to point the name servers to servers THEY control instead of you.
4) When that happens, the government now controls your domain, and can take it offline.
Namecoin was created to prevent all of the above.
It's based on Bitcoin, so all of the same rules apply (peer-to-peer, transactions, miners, blocks, hashes, block chain, etc).
Namecoin, however, has some special transactions that turn it into a peer-to-peer DNS Registrar.
So, you register a domain with Namecoin, you actually OWN that domain. It cannot be stripped from you without your consent, because it's signed with your private keys and the information within it cannot be changed without those private keys.
It does have 1 major drawback: There is no connection from the Namecoin TLD (.bit) to the global Internet. So, if you host a server on a .bit address, only other people who have modified their systems to resolve .bit space will be able to get to those sites.
But, folks are working on that.