If the task is “Everone in Network” then every colleague that follows you will be notified as part of the Main Feed. If the task is “Private”, only the Responsible Persons and Task Approvers of the task will be notified.
If the task belongs to a project the Task Approvers will be informed when a task is complete. However, all members of the project can proactively go and check the task status irrespective whether they are a Task Approver or not.
For more information on tasks go to the Using Tasks article.