The task overview shows all the tasks you have viewing access to in the currently active project, and possibly categorised into different task lists. Viewing access is determined by the groups that have been selected in the permissions tab for each task.
Navigation
At the top of the page is the nagivation where you can create a new tasks and lists (assuming you have permission to do so), perform bulk actions if any of the list checkboxes are selected, and filter the shown data by searching, selecting a milestone, list, author, assigned user, priority or publishing state. The publishing state filter will only appear if you have permission to edit, or edit the state of any task. The milestone, list, author and assigned user filters are only visible when you have an active project - which can be selected next to the search button.
Clicking on a task title will redirect you to the details page where you can see all the information about the item, including attachments and comments.
Task Completition
The button with the tick symbol allows you to mark the task as completed. If the button is highlighted in green, it means that the task is already completed. Clicking on it again will mark the task as incomplete.
Context Menu
The context menu button (indicated by the down arrow symbol) allows you to edit or trash the task. Additionally, you can assign it to a person or change its priority on the fly.
Re-Ordering Items
When you have an active project selected, you can re-order tasks by dragging them and then dropping them again at the desired location. Note that you cannot move tasks from one list to another. You can only re-order tasks within each list.