To mark a task as complete, click the open circle on the List View and a check mark will appear. You can also move your progress slider to Done in order to mark a task as complete when viewing the task on the List View or Board View.
Completed tasks will turn grey and will disappear from view if you have selected to filter out completed tasks in the progress filter.
You can also delete your task by selecting the "..." ellipsis icon to see the Task Details Menu. Completed tasks can always be found in your My Work list.