The iPhone and iPad uses Microsoft Exchange ActiveSync, to push your Mail, Contacts, and Calendar data to your iPhone.
*Note - Setting up these instructions may override any Contacts or Calendars already on the device. Please back those up prior to following these steps as they are not recoverable.
1. Setup your Exchange e-mail account by tapping the Settings icon.
2. Tap Accounts & Passwords
3. Tap Add Account 
4. Tap Exchange
5. Enter your Office 365 email address, password, and an account description, then tap Next
6. If you are prompted to enter server settings, enter the following and tap Next
Email: the full email address
Domain: (leave blank)
User Name: the full email address
Password: the email account password
Server: outlook.office365.com
7. If the Mail app prompts for permissions, tap Yes.
8. Select what you would like to sync to the iPhone and then tap Save.