It’s actually simple. There are two answers.
In a group, a person is always put into a role, it is what others expect of that person. However, what role this is, is not always explicit.
When a role is given explicitly, for example to someone by nominating them into one of the C-Suite roles, then it is the organization that gives that person the authority to exercise his role. It is then up to the person to work on all the organizational needs linked to that role. In essence, It happens by using all the expertise and competence available to organize the work that needs to be done.
The other, implicit, authority is given by the group. It is the authority to lead. It happens all the time and for many reasons. At its best, it results from the group acknowledging that the person leading the team is using their expertise and competence in such a way that they accept to follow. At its worst, it is the circumstances where the group sees no better alternative than deciding to follow and does so out of fear that things could get worse.
However, authority is not enough to be successful. What is still needed, is the ability to align the authority they have been given with the execution of the work.
Authority doesn’t guarantee results. But nothing can be achieved without authority.