Colin Powell says, "Leadership is the art of accomplishing more than the science of management says is possible."
One of the things that sets leaders apart from others is that they are able to get so much more out of the people and its organizations than others are able to. There is something about them that pushes the envelope and pushes the people to do more than they ever thought possible. It is leaders who help people stay motivated and stay on the vision of what can happen when everyone in the organization gets on board of the same goal and starts rowing in the same direction.
In a healthy organization, you have to have both great managers - ones who understand and know how best to make the organization run as efficiently and effectively as possible, and a healthy organization also have strong leaders who are able to lead the organization to do more than what it thought possible.
That's a great definition of leadership.