New law for web site owners and cookies?

[Red Squirrel]

Logged in to blogger for the first time in over a year and saw this notice:

European Union laws require you to give European Union visitors information about cookies used on your blog. In many cases, these laws also require you to obtain consent.

As a courtesy, we have added a notice on your blog to explain Google's use of certain Blogger and Google cookies, including use of Google Analytics and AdSense cookies.

You are responsible for confirming this notice actually works for your blog, and that it displays. If you employ other cookies, for example by adding third party features, this notice may not work for you. Learn more about this notice and your responsibilities.

That explains why I seem to see so many sites that have a cookie notice. What exactly is the nature of this new law, and what type of sites does it apply to? I run a bunch of other sites, and never put such a warning. What are the repercussions of not putting the warning, does the site get blocked in the EU?