To delete your task completely, first you need to complete it by swiping from left to right. To delete and remove the task from the list and into your 'Completed Tasks' list tap thebutton on the right of the task. To remove all completed tasks from the list, shake your device and you will be prompted to move all completed tasks to the 'Completed Tasks' list. If your task is a shared task, shared task members will receive a notification.
Your 'Completed Tasks' list can be found under the Settings tab of your Any.do account.