To date, trying to reproduce a quotable tweet is not an easy task, with the only options being either taking a screenshot and posting the image, or copying the quote and pasting it on your own HTML page. The first doesn't allow for Google and other search engines to index the tweet and the latter leaves out relevant info such as a member's name or avatar.
With the new feature, users can take a quick "snippet" of code that will include the author's name, links, avatar and a panel that allows you to head back to the original author's page.
You can view the Twitter blog post here: http://media.twitter.com/392/tweets-quotes
And an example of the embed (all links work in the original):
Written by: Andre Yoskowitz @ 4 May 2010 1:04