In common usage, leadership generally refers to:
- the position or office of an authority figure, such as a President 
- a group of influential people, such as a union leadership 
- guidance or direction, as in the phrase "the emperor is not providing much leadership"
- capacity or ability to lead, as in the phrase "she exercised effective leadership"
Leadership as a position of authority
In On Heroes, Hero-Worship, and the Heroic in History, Thomas Carlyle demonstrated the concept of leadership as a position of authority. In praising Oliver Cromwell's use of power to bring King Charles I to trial and eventual beheading, he wrote the following: "Let us remark, meanwhile, how indispensable everywhere a King is, in all movements of men. It is strikingly shown, in this very War, what becomes of men when they cannot find a Chief Man, and their enemies can." 
From this viewpoint, leadership emerges when an entity as "leader" manages to receive deference from other entities who become "followers". And as the passage from Carlyle demonstrates, the process of getting deference is competitive in that the emerging "leader" draws "followers" from the factions of the prior "leaders."
In the Constitutional Convention of 1787, the American Founders rejected the idea of a monarch. But they still proposed leadership as a position of authority, with the authority split into three powers, the legislative, the executive, and the judiciary. That is, under the American theory, the authority of leadership derived from the power of the voters conveyed through the electoral college. And many individuals shared in leadership as a position of authority, including the many legislators in the Senate and the House of Representatives. 
Determining what makes effective "leadership"
In comparing various leadership styles in many cultures, academic studies have examined the patterns in which leadership emerges and then fades, sometimes by natural succession according to established rules and sometimes by the imposition of brute force. Some scholars choose to judge the effectiveness of leadership by the size of the following that the "leader" can muster. By this standard, Hitler became a very effective leader even if his promises were delusional and even if his troops coerced the followers. 
Other scholars maintain that an effective leader must unite followers to a shared vision that offers true value, integrity, and trust to transform and improve an organization and society at large. James MacGregor Burns calls this leadership that delivers true value, integrity, and trust transformational leadership that he distinguishes from mere transactional leadership that gets power by doing whatever will get more followers.  But the transformational quality of leadership is more difficult to quantify than would be a mere count of the followers that transactional leadership sets as a primary standard for effectiveness. That is, transformational leadership requires an evaluation of quality independent of the market demand that exhibits in the number of followers.
Leadership as a position of authority, comparison with other apes
Richard Wrangham and Dale Peterson, in Demonic Males: Apes and the Origins of Human Violence present the empirical evidence that only humans and chimpanzees, among all the animals living on earth, share a similar tendency for violence, territoriality, and competition for uniting behind the one chief male of the land.  And the chimpanzees are man's closest species-relative; humans inherited 98% of their genes from the ancestors of the chimpanzees.
In comparison, the bonobos, the second-closest species-relative of man, do not unite behind the chief male of the land. The bonobos show deference to an alpha or top-ranking female that, with the support of her coalition of other females, is as strong as the strongest male in the land. That is, if leadership amounts to getting the greatest number of followers, then among the bonobos, a female almost always exerts the strongest and most effective leadership.
Some have argued that, since the bonobo pattern inverts the dominant pattern among chimpanzees and men with regard to whether a female can get more followers than a male, humans and chimpanzees both likely inherited gender bias against women from the ancestors of the chimpanzees; gender bias is a genetic condition of men. And the bias against women having leadership as a position of authority crosses all world cultures. As of 2002, Sweden had the highest percentage of women in the legislature at 43%. And the United States, Andorra, Israel, Sierra Leone, and Ireland tied for 57th place with less than 15% of the legislature women.  Admittedly, those percentages are significantly higher than the occurrence of female chimpanzees becoming alpha of the community by getting the most followers, but the trends are similar in manifesting a general gender bias across cultures against females getting leadership as a position of authority over followers.
Do certain qualities a "leader" make?
Studies of leaders have suggested qualities that are often associated with leadership. They include:
- Talent and technical/specific skill at the task at hand.
- Initiative and entrepreneurial drive
- Charismatic inspiration - being liked by others and the ability to leverage this esteem to motivate others
- Preoccupation with their role - a dedication that consumes much of their life - service to a cause.
- A clear sense of mission - clear goals - focus - commitment
- Results oriented - every action is directed towards a mission - prioritize activities so that time is spent where results will be best achieved
- Optimism - very few pessimists are leaders
- Rejection of determinism - belief in their ability to make a difference
- Ability to encourage and nurture those that report to them - delegate in such a way as people will grow
- Role models - take on a persona that encapsulizes the mission - lead by example
The skills and practices of "leadership" may compare with management in the broadest sense of that word. In this connection one can view leadership as
- centralized or decentralized
- broad or focused
- decision -oriented or morale-centered
- intrinsic or derived from some authority.
- An effective leader resembles an orchestra conductor in some ways. He/she has to somehow get a group of potentially diverse and talented people -- many of whom have strong personalities -- to work together toward a common output. Will the conductor harness and blend all the gifts his or her players possess? Will the players be happy with the degree of creative expression they have? Will the audience be pleased by the sound they make? The conductor may have a determining influence on all of that.
Leadership by a group
In contrast to tolerating leadership as a position of authority, some highly successful organizations have adopted a pragmatic approach when they found that the role of boss costs too much in team performance. That is, in some situations, the maintenance of the boss is too expensive by either draining the resources of the group as a whole or impeding the creativity within the team, even unintentionally.
For example, the Orpheus orchestra, which has performed for over thirty years without a conductor--that is, without a boss--for a team of over 25 members, has drawn discriminating audiences, and has produced over 60 recordings for Deutsche Grammophon in successful competition with the other world-class orchestras with the autocratic or charismatic conductors. 
Rather than an autocratic or charismatic conductor deciding the overall conception of a work and then dictating how each individual is to perform the individual tasks, the Orpheus team generally selects a different "core group" for each piece of music; the core group as a team work out the details of the piece; the core group present their idea to the whole team; each member of the whole team then participates in refining the final conception, rehearsal, and product, including checking from various places in the auditorium how the sound balances and verifying the quality of the final recording -- all without a boss.
At times the whole team may follow someone, but whom the team follows rotates from task to task among the members that the team finds capable. The Orpheus team even has developed seminars and training sessions for adapting the Orpheus Process to business. 
Other varieties of leadership
The word "leadership" can mean a collective group of leaders, or it can mean the special if not mystical characteristics of a celebrity (compare hero). Yet other usages have a leadership which does not lead, but to which one simply shows respect (compare the courtesy title reverend). Aside from the prestige-role sometimes granted to inspirational leaders, a more mundane usage of the word "leadership" can designate "current front-runners": someone can for a time take over the lead in a race, for example; or a corporation or a product can hold a position of market leadership.
In would-be controlling groups such as political parties, ruling elites, and other belief-based enterprises like religions or business, the idea of leadership can become a Holy Grail and people can come to expect transformational change stemming from the leader; such entities encourage their followers and believers to worship leadership, to respect it, and to strive to become proficient in it. Followers in such a situation may become uncritically obedient. Note the different connotations of a synonym of the word "leader" adopted from the German: Führer. Alternatives to the cult of leadership include co-operative ventures, collegiality, consensus, anarchism and democracy.
Aristocratic thinkers have postulated that leadership depends on one's blue blood or genes. Contrariwise, more democratically-inclined theorists have pointed to examples of meritocratic leaders, such as the Napoleonic marshals profiting from careers open to talent. In similar fashion, traditionalists recall the role of leadership of the Roman pater familias; against which feminist thinking posits emotionally attuned responsive and consensual empathetic guidance.
Many organizations aim to identify, foster and promote leadership potential or ability. See for example the Scouting movement.
Scientific theories of leadership
- Fiedler contingency model
- Leadership participation model
- Path-goal model
- Situational leadership theory
- Trait theory
- Functional leadership model