Exchange Impersonation is used in scenarios in which a single account needs to access many accounts. Line-of-business applications that work with mail typically use Exchange Impersonation. An application can be written to display mailbox data such as number of unread items, calendar, and so on. The application can use a dedicated service account to access multiple users’ mailboxes to display their respective data. While Delegate access is used in scenarios in which there needs to be a one-to-one relationship between users. One common application of delegate access is the sharing of calendars between users, such as when an admin manages an executive’s calendar, or a when handful of individuals working on a project need to coordinate calendars.

Full Article: Exchange API Blog