Open Outlook iOS App on your iPhone device.

Go to Settings >Add Mail Account and select "Add Email Account" (Outlook, Gmail, Exchange, iCloud...).

Enter your iCloud account email address, for example "name@icloud.com" and then select Add Account.

You will then be prompted to enter your iCloud password, at this point you must generate an "App-Specific Password" by logging into your Apple ID account management page, see https://support.apple.com/en-us/HT204397 for how to access the app-specific feature and generate a password. Login to your Apple account from another computer so you can view and manage your app-specific password and input into your iPhone in the Outlook App.

After you have input the app-specific password save your settings and return to Outlook settings to configure additional features. You may add additional non-work email accounts to the Outlook App, some do not require the app-specific password, while others do, this information is not always published clearly at the email providers technical support website. The best method to confirm if a app-specific password is required, login to your email account from a computer using the web interface, go to your account management or security and see if the app-specific option is available. 

AOL (America On-Line) email also requires the app-specific feature to be used.

Useful links:

https://support.office.com/en-us/article/set-up-email-in-outlook-for-ios-mobile-app-b2de2161-cc1d-49ef-9ef9-81acd1c8e234

https://support.apple.com/en-us/HT204397

https://products.office.com/en-us/outlook-mobile-for-android-and-ios