The help page explains more: "The preferred sites feature lets you set your Google Web Search preferences so that your search results match your unique tastes and needs. Fill in the sites you rely on the most, and results from your preferred sites will show up more often when they're relevant to your search query."
Some use cases for the feature: adding sites you trust for finding a certain kind of information (movie reviews, sports results), adding more obscure sites that aren't likely to appear in the top results (local news sites) and a partial replacement for bookmarks.
The feature is an experimental feature that can be found in Google's preferences page if you are logged in and you were selected to test it.
Here's what happens when I add GSM Arena and search for [Nokia 6080]: the result from GSM Arena is marked as "My preferred site", but there's no significant ranking change even though Google mentions that "your Preferred Sites were used to improve search results".
After adding IMDB and New York Times, the results for [how to lose friends and alienate people] were changed dramatically: two pages from nytimes.com were promoted to the top 3 results, but they weren't in the first 30 results for a regular search.
Preferred Sites is an extension of Google SearchWiki, the feature that allowed you to make per-query changes. If the feature goes live to everyone, people will be able to pick a list of authoritative sites and influence all search results.