If you have created a task and you have assigned the task to a colleague then the task will be shown inside your 'Assigned' task folder - that is if you have created the task in the 'In-Tray' folder.
If you have created a task and assigned this to a colleague but put the task into a different folder then the task will be moved to the name of the folder you have entered the task into - and will not be shown inside your 'Assigned' folder.
The 'Assigned' task folder will show you tasks that you have assigned to 'other' users it will not display tasks that have been assigned to you as these will either by inside your 'In-Tray' folder or another folder name you have set up inside your account.