It's fairly complicated. At first, the conflict is between Eragon and the Ra'zac, who killed his uncle. When Brom, Eragon's companion and teacher, dies on the road, Eragon then decides to join the Varden, a group of rebels opposed to Galbatorix. When he comes across a poisoned elven woman, it the conflict his between him and time, as he races across the desert to get the elf her required antedote at the Varden. In the end, there is a battle in which Eragon slays Durza, one of Galbatorix's henchmen.
Overall, the main conflict of the series is between Eragon and the evil king Galbatorix.
Overall, the main conflict of the series is between Eragon and the evil king Galbatorix.