There is an inextricable link between leadership and communication. Leaders are the ones who can clearly communicate their vision. And the ones who can clearly communicate their vision are the ones who can lead.
You do not have to be the smartest guy in the room to be the leader. In fact, it is widely accepted by many historians that two of the smartest men to hold the presidency in recent history, the guys with the highest IQ, were Jimmy Carter and Richard Nixon. Yet, Ronald Reagan, regardless if you agreed with his politics or not, went down in history for having been one of the most popular presidents of all time. He inspired a nation, presided over the booming ‘80s and was responsible for winning the Cold War. He was not known as one of our smartest presidents -- he was known, instead, as “The Great Communicator.”
Follow the link for more analysis and examples.