[benjamincburns]

A lot of the other responses here are too complicated and specific. Here's my attempt to put it into easier-to-digest terms:

In a traditional web stack you have a backend and a frontend. The frontend is the stuff the browser runs, and, simplifying a bit, the backend is everything else.

Ethereum smart contracts basically let you replace your backend logic and database with code that runs on the Ethereum blockchain network. Depending on your application can decide to run only a few parts of your backend on Ethereum, or the entire backend.

It's very slow when compared to traditional backends like nodejs, etc, but it has the benefits of censorship resistance and excellent availability. Better still, you don't need to run or maintain servers to support it if you don't want to (although there are benefits to doing so).

In this case, they're using Ethereum's replacement for DNS, ENS.