Overview
Giving someone delegate access allows them to send and receive emails and setup calendar appointments as if they were you.
Note: The more delegations there are, the more likely they are to be unknown, forgotten or missed, and difficult to identify malicious behavior or even intrusion.
For the IT and Security teams to maintain rigorous control, it is important to regularly check who has access to which mailboxes and whether delegated rights are up-to-date and valid.
Detail
To view the full instructions for delegate access in Office 365, please see this Microsoft support site.