Power
As Winston Churchill said, "History is written by the victors."
For all the powerful people in the annals of history, not a whole lot of that authority or leadership actually trickles down to the history writers. However, historians have power over the narrative; it's their research that frames events of the recent and ancient past, and that's no small thing.
This is way more responsibility than you might think at first. If a historian gets a fact wrong, entire generations may grow up believing in things that never happened, like Columbus discovering America or that aliens built the pyramids (which no legitimate historical society would ever say).
Ideally, historians don't carry much personal bias into their work. It's their job to do the research and present the results in a manner that's clear, straightforward, and impartial (though, admittedly, usually a bit boring). They have the power to omit any information they choose—but that's generally not the game plan.
While historians aren't under strict regulations about their writing, there's a certain ethical standard to live up to when informing the public. People will generally trust a historian's evidence and research because they don't really have any other choice. Just make sure it's all laid out clearly enough to fit into a sixty-minute cable TV show.