Whether or not you receive an email notification when you send a new Announcement or Conversation (what Canvas calls messages sent from the Inbox) is determined by your notification preferences. More detailed information about notification preferences can be found here.
Here's how to update your notification preferences so that you receive an email when you send a new announcement or conversation (inbox message):
1. From the global navigation menu, click Account. Then, click Notifications.
2. Using the Settings for: dropdown, select whether you want to change the notification preferences for your overall account (all courses) or for a specific course only:
3. To receive an email when you send a course Announcement, scroll down to Announcements Created by You. Click on the frequency icon and select "Notify immediately".
4. To receive an email when you send a new Conversation, scroll down to Conversations Created by You. Click on the frequency icon and select "Notify immediately".