There are many definitions of management, and none of them are elegant, but Wikipedia gives us this literal.

Management (or managing) is the administration of an organization, whether it is a business, a not-for-profit organization, or government body. Management includes the activities of setting the strategy of an organization and coordinating the efforts of its employees (or of volunteers) to accomplish its objectives through the application of available resources, such as financial, natural, technological, and human resources. The term "management" may also refer to those people who manage an organization - managers.

So put simply, the co-ordination of people (people are never resources, lest managers be overhead), and resources to achieve outcomes.

What is the difference between a manager and a leader?

At its simplest, people work for a manager, but they follow a leader. You can be a manager without being a leader, and indeed a leader without being a manager. A leader will favour vision over goals, will favour inspiration over instruction, will coach as opposed to direct, and will dig in and get their hands dirty as opposed to telling their teams what to do. A leader shares the journey with their team, and a manager controls that journey for their team.

The best managers are, at their core, strong leaders who happen to have a management position. If you are not a strong leader and have found yourself in a management position, maximising on some of the skills we talk about below can certainly help, but without that focus, you will never be as effective at the role as someone who naturally leads.