Can anyone please clarify the actual relation of the
blockquote element with search engine optimization?
I don't think your find a 100% answer on this question and much speculation but I believe if your pages are THIN with block quote then your most likely be hit by Google panda for duplicate content however if your writing good content which is unique around the block quote element then I believe its a positive.
Many Top Sites use Snippets and Cite Source
I find many of the top ranking websites that are treated by Google with high ranking and high amount of authority more than often use snippets of text and link out to the source, This is completely normal in my Book and I believe it actually helps your rankings because it adds value to your content by offering people more information on the subject as well as like a message this is true look here what this person or site said. etc. So in effect external linking can help your own authority assuming that your linking to other sites with high authority on the same subject.
HTML5 Blockquote is Beneficial
Now I'm not sure if you know but there's a cite attribute in HTML5 which I strongly believe only will be positive for your rankings:
<blockquote cite="http://example.com/all-about-cats"> <p>the quote goes here</p> <footer>— <a href="http://example.com/all-about-cats">All About Cars</a></footer> </blockquote>
I strongly believe by using block quotes as I've said will help your rankings as long as your using your own content on the same page otherwise your not giving any more value than the original source. Additionally you shouldn't quote the whole page either or least I wouldn't give them the option to go there if necessary. Focus on customer experience and don't worry about people leaving your sites, most top sites don't bother about this element, its only usual people who are researching one topic check many sites so nothing wrong with being the middle man if your receiving high volume of visits.
Anyway! as I said its not a 100% answer but used right I believe block quote rocks!
I lost 90% of my traffic over night because of duplicate content and I was able to get all my traffic back by using Blockquote with the cite attribute, but also increase by traffic by +82.5%.
I wrote a blog post with all data, traffic changes and graphs here (http://condopilot.com/blog/marketing/how-i-increased-my-traffic-825-after-being-penaliz/) and you can clearly see that the blockquote-attribute makes a huge difference.
The great thing with it is that you can mark a small part of the page as "Duplicate Content" instead of having to mark the whole page, as you do with a rel="canonical" tag.
Ideally, you should have enough content to distinguish yourself from other related content. Mentioning, referencing and quoting content from other websites is actually encouraged if it adds tot he top of conversation.
In cases where your content is nearly identical to another site, Googlebot is intuitive enough to decide where the original content stems from and thus, will show that site on search results.
Taking a quote from another site is a great way to encompass multiple perspectives on the topic at hand. It really doesn't matter whether you use "blockquote" tags or not.
Ultimately, if the majority of your site's content is other people's work/ideas, the Panda algorithm will find you.
Bottom line: Keep it original and supplement with useful references to add more value to your perspective.
More info here on John Mueller's take on duplicate content