Pie's new. It's a combination of a way for people to fund the empire and show appreciation to other forum members for things they do. It's nice to have a way to recognize exceptionally helpful or informative permies. You can buy a pie (or just a slice) and link for that is at the top of the page. You can give away your pie (link for that at the top right of each post) and you can receive pie from others.
There's a few perks (access to a special forum, product discounts, extra forum privileges) that come with having pie. I expect many more to accumulate over time.
Apples can only be given out by people with special privileges gained by taking on responsibilities like moderating the forums. I'm not sure who everyone is with that power. Like the pie it can be received for helpful forum posts, but it is also awarded for off forum assistance to Paul's
World Domination goals. If you get
enough apples (I think it's 15 right now) you are allowed to visit the cider press where discussion of highly controversial topics is allowed.