Just in case anyone is not up to internet speeds, Google owns the internet. It's a fact. Whether you like it or not, they literally make millions a day (printing money) on many channels, but notably, the Google AdWords system. Google essentially sells traffic based on your keyword query and clicks in Ads. But wary of the non-evil machine, you cannot do the same on your website. Hence, the heavy handed rules that Google imposes comes into play with the follow, no-follow directive.
This simple modification of a link on your website is critical to giving "link juice." If you add a link to your website with no modifications, it will give link juice to the destination website. All websites want these type of links because they are the best of "Backlinks"... one of the top indicators of website value, according to big G. This change, now suggesting the "no-follow" is just a hint, and not a clear directive, opens up the door to impacting billions, yes, billions with a B, websites. It may be a SEO killer. Google has always attempted to continue to reduce and minimize the organic SEO rankings. Google does this by adding location maps, suggested places, reviews, etc. Google would love to just push all organic rankings off page one, if they could with no user impact.
However, the no-follow change isn't too new, it was announced last year and Yoast talks a bit more about it in simple terms here.