What Is Google RankBrain And Why Does It Matter?

Recently, Google made another one of its fascinating yet painfully ambiguous announcements: the company is now relying on the power of an artificial intelligence system known as RankBrain to monitor its search results, make progress where necessary, and ultimately guide the development of their core search algorithm. In fact, over the past several months, a "substantial percentage" of all Google queries were handled by RankBrain itself. The average user (i.e., people like you and me) hasn't noticed anything especially different, but according to Google's plan and current available data, this move to RankBrain will make the web an easier, better place to search. That being said, if we haven't noticed much of a difference, why is RankBrain such a big deal? What is it actually doing, and why is that relevant to the average user?