Delegation in Project Server and Project Online is an extremely powerful capability that can be used in numerous situations. For support situations, help desk personnal can use it to login as someone experiencing a permissions-related issue to confirm, research and resolve an issue. In a project team situation delegation can be used to submit time for a Team Member who is out sick or on vacation, or to accept time for a Project Manager who is away attending training.
This training video is key to gaining a solid understanding in how to leverage the Act As Delegate feature in Project Server & Online. Once a delegate is created, the next step is to leveage that delegate using the Act As Delegate function, which this video covers. Therefore be sure to watch session 1 of 2 on Delegates: Manage Delegates, to complete your understanding of this very useful functionality.