It is still a little early to get any deep analysis of this latest update but early reports are that this will improve search quality for end-users by understanding questions and their meanings a lot better than before.
Prior to Bert Google used stop words so words like "to, and, it, or" were mostly ignored. However, this created a bit of a problem for Google as a small word like to can and does alter the meaning of a question quite drastically.
It's aimed at fully understanding a user's question and then matching it with the correct results from what I understand so far is the goal of this latest update.
It's no longer just blindly word matching to get results, it's about a deep understanding of the language. I believe this rollout is aimed only at English currently so not all websites will see much change. However, I have read 1 in 10 websites will be effected in search so this is quite a major development.
Time will tell however as we learn more about it.