Plot hole: If Noah could be brought back from the dead with Claire's blood why couldn't they bring back Nathan? Was turning Sylar into Nathan really the first thing they could think of?
Continuity mistake: When Sylar is impersonating Nathan, the knot on his tie keeps changing between scenes.
Chosen answer: It's not been made 100% clear. It was originally assumed that he actually consumed part of the brain, but this has turned out not to be the case. Sylar has been shown all along to have an instinctive knowledge of how things work and how to fix them - this is his actual original power and the ability that made him an exceptional watchmaker and repairer. It appears that he uses a similar process when acquiring new powers - he exposes the brain of the target, allowing him to examine it and determine how their power functions. He can then apply that knowledge to his own brain, allowing him to replicate the ability in question.
Tailkinker ★