Brave sells ads. They get $X normal money from it. The ads are delivered from a local catalog downloaded in bulk (the same way safe browsing blocklists are, for example) and matched on device.

If you opt in to see Brave's ad popups, you get a cut from the revenue those popups generate.

Brave gives this cut as BAT - they buy the coins from the open market.

Brave has a built-in tipping service where you can tip people with BAT. If you do, Brave transfers BAT from your wallet to the tippee (and Brave takes a cut from the transaction).

Tippee has BAT that they can sell because there's at least one buyer of BAT on the market: Brave.

It seems like a sensible system overall, but my specifics may be wrong.