It is a place where you can view the new activity in the projects and tasks you are following. You will also receive info about the latest projects there.
The blue dot disappears after you open the task with a new activity. That means you have already read the activity in this task. When you go to Activity view again, the app will not display that task on the list until your teammates make the new activity in the task. When you enter such a task from a different view, the blue dot also disappears. You can also mark this task as read with the blue “read” button on the task list. Tasks in the Activity view are grouped by project. You can also use the blue “read” button next to the header with a project name. It will mark all tasks in this project as read.
You can also use gestures to manage your tasks in this view. Swipe on a task to the left to go to the project the task belongs to. Swipe to the right to mark it as read.