The idea, as stated on the host's blog, is 'to share the first sentence (or so) of the book you are reading, along with your initial thoughts about the sentence, impressions of the book, or anything else the opener inspires.' There's a hash tag #BookBeginnings for twitter etc too, and a master linky list on the host's blog. I've got a couple of books on the go at the moment so I've just picked one out to mention here.
Published by Weidenfeld & Nicolson
What an intimate and detailed first few lines, quite vividly introducing the man who will be the main character in the novel. I've just started this one and it's beautifully written so far.