The BAT platform is entirely opt-in, so users can browse with Brave as they currently do without having to enable ads. So, will they? Many will, and for a variety of reasons:
The financial incentive (earning/spending BATs): whereas the conventional browser today offers the user zero financial reward, the Brave browser offers the user something of value, be that $10 per year, or, as Brendan Eich has speculated, well upwards of $100. Assuming something in-between, having those funds available could pay for your news subscriptions, tipping content your favorite creators or the odd donation to your cousin’s half marathon. (In fact, simply having a payment method that doesn’t involve having to trust another third party with your credit card data would be an incentive to utilize BAT in and of itself).
The financial incentive (speculating on BATs): many users anticipate that the token value could appreciate dramatically, assuming widespread or even just niche adoption. Much like countless users mined cryptocurrency on their modest home computer, the next generation of bedroom speculators may well browse their way to a BAT position.
The novelty factor: the ads that are will be running in Brave are not the same that the user would encounter otherwise. If not for anything else, the sheer novelty factor of these ads may entice quite a few industry aficionados (and these should represent a good portion of the initial community of the 5.5 million users already amassed).