Delegate access allows another user to send mail using your address and also create/edit events in your calendar.
It is often used if you are looking to give access to your Executive Assistant (EA), or you are supporting a member of staff and require access to both their calendar and mailbox.
Please see the following page:
https://support.microsoft.com/en-us/office/about-delegates-allow-someone-to-manage-your-mail-and-calendar-41c40c04-3bd1-4d22-963a-28eafec25926
Unless there is a specific reason, no-one apart from yourself should have direct access to your mailbox/Calendar. If you are asked to share access to your mailbox/calendar by someone unknown to you (either inside or outside LSE) or you were not expecting the request, please contact LSE Tech Support.