The Delegation lists are lists of Tasks and Leads that don’t have an owner.
How to move Tasks/Leads to Delegation lists
If you click on Delegate a Task or a Lead you can leave the Delegate to fields empty, then the Task/Lead will be moved to the Delegation list.
If a user declines a delegated Task/Lead it will end up in Delegation list.
If automatic Task has not been handled before the deadline is reached it will automatically be moved to the Delegation list.
How to assign
Assign to me:
When clicking on Assign to me, you take the ownership of that specific Task or Lead
Click Assign if you want to delegate the Task or Lead to someone else. Choose department and user to send the Task or Lead to.
When a Task/Lead gets added to the Delegation lists all users will get a notification that a new Task/Lead is available.