According to a (now-deleted) project page discovered by ZDNet, the Bali project is based on the concept of inverse privacy. If there is information that only you have and no one else does, that is private. If there is information that someone else has about you but you don't have, that is inversely private. According to Microsoft, its goal is to reduce inverse privacy to a minimum.
In order to do that, it is creating Bali, a "personal data bank" that puts users in control of any and all data collected about them. Any information that a user generates will be stored in the bank and the user will have the ability to view and manage that information. They will even be given the choice to share and monetize the data if they so choose. That makes the feature a bit different from similar offerings from companies like Facebook and Google, which allow you to browse data collected about them but offer more limited control.
Not much else is known about Bali for the time being. The project is described as being in its initial stages. There was a page for Bali where early testers can enter a code to access the project and people without a code can request one, though Microsoft appears to have removed it since this article was first published. Engadget reached out to Microsoft for more information regarding Bali and will update if we hear back.
Update, Jan 5th 2019, 6PM ET: This post has been updated to note that Microsoft appears to have pulled down the Project Bali beta sign-up and info pages.