If you enable BATify by switching the "Status" switch to "on", BATify stores for every website you visit the domain name and the duration of your visit.
Where is the collected data stored?
The data is stored locally on your computer in the storage local area of your browser.
Why is this data collected?
This data is needed for the contribution to the websites you visited.
How is the collected data used?
Once per month a contribution process is started where based on the collected data a voting takes place. The voting result is then transferred to the Brave ledger server using the Anonize2 protocol (https://github.com/brave-intl/bat-ledger/blob/master/documentation/Ledger-Principles.md). Anonize2 makes it impossible for you ever to be identified based on the sites you voted for.