Why is this person chayov in the korban and then the Gemara saying that " Yom Kippur" absolves from bringing the korban he's chayov in?
Daf yomi darchei Noam , Northbrook,il.
1. The Korban referred to here is an "Asham Taluy" -- literally a "hanging Asham." This Korban is brought by one who is unsure about whether he transgressed a particular sin. For example, if there were two pieces of meat on the table, one Kosher and the other one Tereifah, and somebody ate one of the pieces but does not know whether he ate the Kosher one or the Tereifah one, he must bring a Korban Asham Taluy since he is "in suspense" ("hanging") about whether he committed the transgression.
2. The Mishnah later (25a) states that if one is certainly liable for a Korban, he must bring it even after Yom Kippur passes. However, if one was obligated to bring an Asham Taluy and Yom Kippur passed before he offered it, he becomes exempt. The Gemara (end of 25b) derives this Halachah from the verse (Vayikra 16:30) that says that Yom Kippur atones "for all your sins before Hash-m." This means that when only Hash-m knows whether or not the person sinned ("your sins before Hash-m"), then Yom Kippur atones without a Korban.