One can be a leader only when one desires something to happen in the world. This something can be called "change". Leaders want to change the world (or a part of it) in some way.
The change that a leader wants to see in the world - the impact they want to make - that is their vision.
Having a random vision isn't very helpful. A successful leader has a vision that is borne out of the needs and wants of the humans around them. A vision that is rooted in humanity. One that benefits the human kind.
A leader effectively communicates this vision to others, in an attempt to inspire others to work towards the same vision. The quantity of how much a leader is able to inspire action could be the measure of someone's leadership.
Such communication can occur in many ways - through talking (sometimes even story-telling), writing, or through setting examples. When a vision is completely new, leaders are forced to communicate more verbally. But when the vision has already been articulated (by other leaders, for example), leaders can inspire by setting examples through their own work.
Change requires work (often hard work). One person can only do so much work. Leaders create coalitions with people to get more work done towards their vision. These coalitions can look like organizations, companies, networks, groups, actual coalitions, etc. We could call them movements. Leaders lead movements.
Movements may have strategies, planning, coordination, structure. And these keep evolving with time, based on the real world position of the movement.
At this point, one may ask, is leadership hierarchical? Should there be one leader (or a hierarchy of leaders) for one movement?
Before we answer that we will have to answer a related question - Is everyone a leader?
The romantic answer to this question is that everyone is a leader. But that's similar to saying all human beings are equal. Everyone can be a leader given the right circumstances. And everyone should be a leader. But everyone is not a leader. One becomes a leader only when one is able to accomplish a vision through leadership as stated before.
When one looks at leadership with such raw sincerity, we will see that the stronger leaders automatically are able to get more work done and a hierarchy is inevitable no matter how hard we try to avoid it. Saying this hierarchy doesn't exist is like erasing caste/race/class from our society.
A slightly more romantic way to look at it is by imaging every individual as a leader of their own movement - where movements overlap with each other significantly. Each individual can be thought of as a celestial body with their mass (leadership capacity) determining how much gravitational pull they exert towards their vision on the people around them. The most massive leader will have the strongest pull.
Consequently, if everyone are equal leaders, there would be no hierarchies and vice versa.
There are social, economic, and political determinants for any individual's leadership mass. Someone born with privileges - of caste, gender, sexuality, class, race, disability, and others - might find that their leadership mass is already greater than someone without those privileges. In many situations, for example, money speaks. And someone with money - or access to money - might have it easier to "lead" others. Social capital is another example.
Leadership mass can increase (and decrease) over time. This can happen through education, scholarship, credentials, affiliations, positions, jobs, work, association, mobilization, agitation, talking, writing, creativity, relationships, etc. Even gaining a follower base on Twitter can increase someone's leadership mass (through psychology of mass appeal).
This leadership mass is called "power" in the formal language. While vision determines the direction a leader pulls people in, power determines how strong the pull will be. It is impossible to be a leader without power (of some or the other kind).
This is where things get intensely human and psychological. Power works through human emotions. Fear, love, hatred, joy, laziness, anger, sorrow, confidence, trust, aggression, etc. But not every human has the same emotion when confronted with the same stimulus. An anti-establishmentarian will look at you with scorn when you tell them that you're from the ministry (of whatever) whereas someone who is awed by such positions will be psychologically receptive to what you want to say. It is safe to say that most people will be pulled by mainstream sources of power (because majority acceptance is what makes these sources mainstream).
Effective leadership thereby also becomes a performance. Like doctors need to be chameleons and be the doctor that each patient needs, leaders will have to be the leader that each individual needs. If someone is motivated by solving complex challenges, the leader can get them excited by presenting their vision as a complex challenge. If someone is interested in creative expression, leader can find avenues for creative expression that advances their vision.
At this point, the conscientious reader will ask whether leadership is emotional manipulation.
Manipulation has negative connotations. Perhaps "emotional guidance" captures the nuance of what leadership does with emotions. Leadership is about emotionally guiding people. There can be effective leaders with selfish motives and they can turn this into manipulation and abuse. But you can't blame any individual for being too sincere towards their own vision, albeit a bad one.
Also, the human mind is trapped such that it can never be free of influences. Everything that happens, every interaction, every thought, every idea - everything changes the mind. And therefore, the only way someone can never "manipulate" your thoughts is by never coming in contact with you.
The same reader will also ask whether this view of leadership considers people (followers) as lacking agency (autonomy).
In this world, nobody has complete agency. Every human is delicately dependent on other human beings in this society. Complete independence is not possible for any human. And therefore, a transactional view of individual relationships where every relationship is that of giving and taking models the society in a better way.
Considering the sensitive nature of the relationship that a leader has with others, it is very important that leaders are empathetic and emotionally intelligent. Leaders must be quick to identify an emotion, to label it, and to address it. That includes self-awareness and awareness of one's own emotions. They need to think of things from the perspective of multiple others and bring those perspectives together in their vision.
This empathy also gives leaders humility. That they do not know all the answers, and that their answers have to include all the perspectives from people around them. That if the answers did not entrench empathy this way, they wouldn't be able to achieve their vision. That it is unlikely that one human being's vision is greater than everyone else's.
An intense desire to create more and more powerful leaders around them arises in leaders from this humility. They see that the world is better served by a multitude of visions and that for each vision to succeed there must be leaders taking those visions forward. They strive to turn people around them into leaders who can pull weight. That's how the best leadership is scalable - by being infectious.
When enough leaders pull weight in the same direction, no vision is too far to achieve.
Why does the world need leaders to pull though? Can't well articulated vision statements automatically attract people?
Inertia is the problem. Human beings are resistant to change - individually and as a society. It might be explained by evolutionary psychology. Human beings have evolved past the stage where they need to be held hostage by biology, yet we are biological beings. And we are not rational beings by design.
If we were rational we wouldn't have problems like global warming, poverty, and war in our world.
Leaders appeal to both the irrational and the rational sides of human beings at once. That's how they pull people out of their inertia. Once people are moving, systems move too. Especially if you pull the heavier people.
Leaders, hence, are balancing-artists. They have to handle conflicts all the time and find balance. There is strategy, but there is vision. There is rationality and irrationality. There is movement and there is stasis. There are tensions and counter-tensions. There is pressure to lead and pressure to follow. Leaders make judgement calls all the time. They can go wrong many times. And over time the number of right calls decide whether they become effective leaders or not.
Is leadership a teachable/learnable skill?
Leadership requires a lot of practice. But it is also important to know what to practice. That is where the learning/teaching part of leadership lies. There are plenty of books written about leadership. Plenty of stories to read and learn from. Concepts like "ownership", "thinking big", "delivering". Almost every major (successful) organization has leadership principles which have been documented. Exposure to leadership philosophies can accelerate someone's growth as a leader. Consuming content about leadership helps think in different ways and gain new perspectives.
What now?
Think about whether you have a vision for the world. Think about how effective you are as a leader in taking the world towards that vision. Talk to people around you about leadership. Read. Find avenues for your own growth as a leader. Find people with similar values and vision. Grow each other. Grow yourself. And change the world.