I understand it to be limiting the type of information apps are allowed to track about you. Specifically, they shouldn't store your UUID.
For example, apps could associate your UUID with behaviors you demonstrate in the app and so provide targetted marketing. The idea of behavioral tracking and targeting are discussed on this World Privacy Forum page.
The upshot is that if you enable privacy, apps shouldn't provide tailored (targetted) adverts to you based on what you do in their apps. I'm not sure how it'll be enforced though; perhaps, it prevents access to your UUID, but I'm not sure if that'll be for iAd apps only.
The "Learn More" link at the bottom of your screen gives some explanation in Apple's own words. The non-personal reference I think is about anonymising your UUID (so it can't be traced back to you personally) but in essence its still a UUID.
I amI'm sorry I don't have more specific information about the implementation but hopefully this sets the scene somewhat.