Antifeats are from Kingdoms of Kalamar's Villain Design Sourcebook. You get 1 antifeat (chosen at random) every level that you choose to take an antifeat (read: every level), and you gain a bonus feat of your choice for every 2 antifeats you take. The bonus feats and antifeats are unrelated.
Since the antifeats are determined randomly, it's very likely that you'll get antifeats that don't apply to you, which makes them awesome. For example, my Shadowcraft Mage has the Psionic Fist antifeat, which means that if he had power points, he could spend them to reduce his unarmed strike damage. Just to be clear, he does not have power points.