Looking at the Payments tab under Brave's preferences helps to clarify the blockchain aspect quite a bit. Basically: Brave Payments is an attempt to replace the necessity of running advertisements for publications you visit to pay their bills and feed their staff. The BAT token, which is traded on markets and holds value, is used to make micropayments to publishers who's work you're viewing online. These numbers aren't accurate at all, but, for example: You load 50 BAT into your browser's wallet. If you spend 4 minutes reading an article from TheFutureOfNews.eth, you will transfer 0.1 BAT to that publisher. This way, incentive is created for work to be created and viewed, without the need for obtrusive advertising in between the viewer and creator.
As the BAT token and Brave browser are a web3 project, the proper place for the question would be over at https://ethereum.stackexchange.com/ .