For example, with T-mobile, I can register my credit card, and if I use that credit card at any of the participating outlets, I can earn cashback. Similarly, if I register a non-Bilt credit card with Bilt, then I can earn Bilt points on ‘eligible spend’. How are they able to access my credit card transactions? and are they getting access to only the participating outlets, or all of my transactions? and what do they gain by doing these schemes other than increasing their brand value?
The ToS and privacy policy will give you an actual answer. Generally, you are having all of your purchases and stuff tied to your name, age, gender, address (approximate or specific maybe), and other demographic data. This data is then used for a variety of purposes running from actual research on trends and such to targeted ads, to who-knows-what. Basically you and your data are the product and you get points for being so.
Grocery store cards were one of the early adopters of this sort of thing, IIRC.