Leaders are leaders because they inspire the people who work with them. Those people want to work with leaders because they like them, feel challenged by them, and respect them. They are happy to be followers of the leader because they can learn from them and feel as though they have accomplished something good.
What inspires people to follow? There's many parts to that. Respect, admiration, desire to learn, a yearning to be associated with someone and their success, as well as a need to be in a team (although engineers, perhaps more than most of the general public, can function well as individuals). But most of all, people want to follow someone who is going to be a role model, someone that person wants to emulate or at least partially absorb the character from. It seems perhaps self-evident, but leaders give a sense of hope and a potential for success to followers. If they follow, they will be part of a much bigger dream or successful project, and some of that will rub off on them. No one wants to follow someone who they think cannot inspire.
But how do you inspire people to follow you? Well, that's a complex subject because it depends on the kind of inspiration. When I first started working at a company in Vietnam, I was told by one of the engineers that he felt inspired by me because I was "a nice guy" while all the other bosses were demanding and overbearing. It may be the amount of work someone accomplishes, which others are in awe of. A very technical person can be an inspiration to others who want to learn new things, and move their professional knowledge along. Perhaps it is the sense of vision and architecture, and followers can marvel at the "big picture" the leader seems to see so clearly but which remains opaque to them. Sometimes it's the "rule the world" vision (or at least the team, the group, or the company) that makes a follower feel part of a much bigger success, hoping some of that is attributed to them. Perhaps it's the sense of admiration for someone's character, or some trait about them that others admire such as the ability to keep cool and collected when surrounded by panic. It may be the honesty and trust sensed in a leader, knowing they will not abandon or belittle the followers. There's a lot of things factor into inspiration and everyone is inspired by slightly different combinations. What is clear is that most leaders have several of these things going for them.
I doubt you can learn to be an inspiration. It seems to come naturally in all those I have admired and respected. It may be earned, but it isn't automatic either. You can build the ability for inspiration, to be sure, by figuring out which attributes you really want to concentrate on and which are beyond you. Technical inspiration comes from knowledge and can be built. Inspiration from trust can be accumulated by being an honest, open, caring person. Other aspects can be learned or earned in time, but some are difficult because they may go against a person's nature. Learning to inspire, though, is usually not a task you can set and develop, it comes about naturally, sometimes with time, but usually with experience based on personal nature.
Leaders can also be inspired by others. I have often marvelled at the skills and talents of my team members and tried to learn from them, which inevitably means I become a better leader (if I do it right). In fact, I'd go as far as to say a good leader should always be getting better at inspiring others, and as time goes by that does seem to be the case.
Personally, I've been inspired and learned to lead from many different influences, some professional and some personal. I learned how to be open and honest from my personal life. I learned how to be a technical inspiration by some of the very clever people I've worked with or read about. I learned to be a hard worker from my upbringing. I learned about character from many sources. In all, I've tried to learn something important continually, hoping it will make be a better leader and that I can inspire others to follow.
But it is clear that without the ability to inspire others, you have little chance of being an effective leader. So whatever magic is involved in the inspiration, it is obvious quickly to others in the way you interact and deal with them. And the best leaders all do inspire others around them.