To try this feature, make sure that you are using google.com in English. Click on a search result, then go back to the list of results. You'll notice that there's a new link next to the result you've just clicked: "block all [domain.tld] results".
If you block an entire domain, you'll no longer see results from that site. You'll only notice a small box at the bottom of the search results page which informs you that you've blocked certain results.
There's also a page that lets you manage your blacklist and manually block sites. "Sites will be blocked only for you, but Google may use everyone's blocking information to improve the ranking of search results overall. You may block up to 500 sites."
As Barry Schwarz points out, blocking sites is not a novelty: in 2005, Google tested a similar option. "If you're in this experiment, you'll have newfound powers. Click the 'Remove result' link and with one click you can drop that url from your search results. By default, it will only block that url for that particular search. If you're really annoyed, you can click 'More options' and you'll get two more choices: block this url from all future searches and the ability to block the entire host from all future searches," explained Matt Cutts at that time. The experiment wasn't successful, but Google partially resurrected this feature in SearchWiki: you could only hide a search result for a specific query.
I think that blocking an entire site from Google's results is a feature that's way too powerful for a regular user. Some might use it accidentally and find that Google's results are suddenly less relevant. Google could add a link for explicit feedback ("Not useful?") and use that information to personalize search results.