Cross-app activity can't be tracked without this permission. So if you see an ad for a product on facebook, then you pop over to Safari, search for the product, and purchase it, facebook can't attribute that sale to that ad.
The consequence of this is that goal attribution (like sales) for ads is harder, so FBs models can't learn as well who would be interested in the products. You'll see less relevant ads and companies' cost of customer acquisition will go up.
It's easy to imagine a world with less effective ad targeting since most media doesn't have effective targeting. Think pharmaceutical commercials on TV.
My own bias: I run a niche D2C brand whose business model got wrecked by this change!
Apple disallowed third party cookies (like all other browsers) so now your website with Facebook embedded can only tell Facebook "I got a visitor" and Facebook has no data on who that user is (since they look to be logged out). Before third-party cookie blocking was a thing, Facebook could track users if they were logged in on the web, and thus could potentially attribute the sale to an ad that was shown in Facebook itself.
If the user clicked the link in Facebook for your ad, then popped over to Safari by clicking the "open in Safari" button then Facebook can continue to track that because they saw the final click and can add query parameters on the other end that you can send to Facebook upon checkout completion.
What Facebook can't track now is when a user installs Candy Crush, Quit Smoking app, and Instagram... thereby limiting what ads it can show a user in Instagram to just the behavioral data they get from Instagram, instead of knowing the user also has Candy Crush and a Quick Smoking app (and thus would likely be interested in quick games and cessation of smoking stuff).
If that's the case though, I'm a bit confused as to why attribution got so much worse. I'm seeing 50% attribution dropoff.
1. You're on a website about pets, which has FB code on it: Facebook can't link that activity to your account anymore, which means they'll have less accurate info about you that might be relevant to advertisers.
2. You see an ad on Facebook and then go to that website to make a purchase -> FB can't link that purchase to your profile and as such a) can't tell the advertiser whether their ads are effective b) can't use that data to optimize the campaign for users like you who might also be likely to buy.
2. Within the Facebook app if you click a link and make a purchase they can absolutely still track you. If you click a link and open it in Safari, they can still track you.
If however you see an ad on Facebook and search for it in your browser without clicking any links then Facebook can't track you, do to third party cookies being disabled.
https://www.nytimes.com/interactive/2019/12/20/opinion/locat...
If you go further you can probably find hundreds more interesting data points like constant location tracking or full access to any media file mixed with face recognition software.
In short: Your phone is a goldmine of information not only on yourself but anyone you know.