RankBrain is a component of Google's core algorithm which uses machine learning (the ability of machines to teach themselves from data inputs) to determine the most relevant results to search engine queries. Pre-RankBrain, Google utilized its basic algorithm to determine which results to show for a given query. Post-RankBrain, it is believed that the query now goes through an interpretation model that can apply possible factors like the location of the searcher, personalization, and the words of the query to determine the searcher's true intent. By discerning this true intent, Google can deliver more relevant results.
The machine learning aspect of RankBrain is what sets it apart from other updates. To "teach" the RankBrain algorithm to produce useful search results, Google first "feeds" it data from a variety of sources. The algorithm then takes it from there, calculating and teaching itself over time to match a variety of signals to a variety of results and to order search engine rankings based on these calculations.