RankBrain is a part of Google search algorithm which uses Machine Learning(ability of machines to learn and apply) to provide better results in next search.
How does it matters?
It matters in way to improve search results on Google. It learns what a user prefers after searching and when next time anybody searches, applies that. If it is not used then users will get same results again and again which is less interesting than getting improved results. Thus with RankBrain, more user will prefer Google search.