In Reiki, "master" (or Shihan) does not mean someone who has finished learning. It marks the point where a practitioner takes on the responsibility of passing the practice to others.
What "master" means
The title can be misleading. A Reiki master is not a person who has mastered some hidden power, but one who has committed deeply to the practice and can now give attunements and teach. Humility, not mastery in the everyday sense, is the quality most teachers hope to see in it.
The path there
The master level is the third degree, reached after the first (Shoden) and second (Okuden), usually with time and steady practice in between. It involves receiving the master attunement, learning the master symbol, and — in most lineages — being taught how to attune and teach others in turn.
Master and teacher
Some lineages separate the master level into two stages: an initial master degree focused on deepening one’s own practice, and a further teaching level for those who will actually run classes. Not every master chooses to teach, and there is no obligation to.
A considered step
Becoming a master is best taken slowly and for the right reasons — a genuine wish to serve the practice, rather than to collect a title. Many teachers encourage a good stretch of second-degree practice, and honest reflection, before taking it on.
Beware anyone offering a "master in a weekend" as a quick credential. The level carries real responsibility, and is usually the fruit of years, not days.