Microsoft has announced that the native Mail app (Mail.app) on iPhones and iPads that have upgraded to iOS 11 is not functioning as expected as users are unable to send or reply to email. Users can send or reply to emails using the web-based Office 365 email application or by installing another email application until this issue is fixed. At this time, Microsoft or Apple have not announced a solution.
Note: These issues don’t occur in iOS 10.
For more details see the Microsoft announcement: https://support.microsoft.com/en-ca/help/4043473/you-can-t-send-or-reply-from-outlook-com-office-365-or-exchange-2016-i