Leadership is pretty difficult to define. A few years back I made a bet that I could produce 10 different legitimate definitions of leadership, but delivered an even dozen without any difficulty. The word "leadership" is searched an average of four million times a month and produces more than one hundred million pages. (For comparison, "American Idol" is searched an average of 14 million times a month and produces two hundred million pages)
The Online Etymology Dictionary doesn't even have an entry on the subject, and has very little to say about "leader." The Random House Dictionary and the Merriam-Webster Dictionary can't seem to define it without using the word "lead."
Congratulations must be given to the American Heritage Dictionary for providing "guidance and direction" instead of just "the act of leading."
There is a particular trend in the introductions of attempts to define leadership, as illustrated by the Business Dictionary, About.com, and even Wikipedia that is best summarized as "no one's really sure but here's what the consensus seems to be." People and organizations are usually careful to state that they are providing their view on leadership, which they might be quite confident in, but which they will not claim is The Definition of the word.
I think that leadership is, quite simply, the act of dealing with change. I think this is The Definition, and that it has been missed, because there isn't much more one can say about it. The general consensus definition of leadership is usually something along the lines of "inspiring a group to action." However, this is almost always qualified with a list of additional actions that should be included, and a caveat that even then the definition is probably incomplete (and even when the definition is complete it shouldn't be taken strictly literally).
Working from that definition, then, it makes sense that it would be misunderstood. Because leadership is dealing with change, unlike management which is dealing with complexity, the act of leading is basically just guesswork. There isn't much more you can say about it. Take what you know about a situation and try to predict the future; you'll be wrong sometimes and right sometimes and hopefully you'll get better. Now, the position labeled "leader" does require an array of skills like management, communication, character, etc because once the guess is made it becomes a mere comlexity challenge, which can be managed. Management can be explained, so that is what gets explained, because the leadership part of it actually takes very little explanation.
I went into more detail in this post.