The primary use case for BAT seems to be a micropayment scheme that replaces ad revenue. Of course, micropayments are still payments and people still don't want to pay for content, so you can also pay them (in BAT) for watching your ads, and then they can spend those BAT somewhere else.

As dubious as I am of cryptocurrency in general, display advertising is evil and needs to be destroyed, and BAT is the best (only?) micropayments alternative out there, as far as I can tell.