Leadership is well defined - that's not the problem - the problem is it has many, many various definitions. Leadership definitions change throughout time. Your grandfather's definition of leadership may vary quite drastically from your's - ask him if you have the opportunity.
A modern classic definition:
Leadership is a process whereby an individual influences a group of individuals to achieve a common goal. -- Peter Northouse
A brief history of Leadership
A working definition of leadership
Is leadership a process
May leadership emerge from a group
Is leadership more than a form of coercion and power
Various Leadership Approaches
Situational, Skills, Style, Trait
Leader-Member Exchange Theory
Transformational Leadership Model
Servant Leadership Model
Authentic Leadership Model
Team Leadership Model
Disclaimer: as this blog is a from of note keeping for me - an extension of my cognitive model of the universe of knowledge - this article and the series of article may be in great flux until complete (or good enough to quit editing).
1) Leadership Theory and Practice - 6th Ed. by Peter Northouse.