A task board represents the visual information of work in progress. It shows how much work still needs to be done, how much work is in progress, and how much work has already been completed. Every Scrum team day starts with the daily standup status in front of the task board, covering basic questions of how much work each team member has finished since the last meeting, and what work will be in progress till the next meeting, and if there are any impediments.
To answer the question of what makes a task board a great one, we need to understand a typical day in a developer's life, the team dynamics, and a bit of high level view from project a and organization perspective. Some of the requirements from a task board which differs from one to another are:
Alignment to the development process
Prioritized backlog of Story and technical tasks