The Active tab displays the list of uncompleted tasks that are assigned to all users of a group or groups. The main purpose of the tab is to display the list of tasks, so that you can track the execution of tasks.
Only those tasks are available to the Workflow Owner where the Workflow Owner himself (1) or the group he is a member of (2) has been assigned as the executor.
You can learn more about each function and button, as well as how to work with the Active tab here: