DayBack doesn't have any email notification logic itself, but it will honor the notifications you've set up in Google Calendar, Salesforce, etc.
Email Notifications in Salesforce
Sending Notifications and Invitations from DayBack
Email notifications aren't built into DayBack but notifications you've set up in Salesforce will continue to work with events you're editing in DayBack.
To send an invitation or notification for an item in the calendar you'd first get the invitation working in Salesforce. Normally this is done by creating a trigger based on a field in your event or custom object: when that field is modified, the trigger will send an invitation. We've seen users create a new checkbox field called "send invitation" that is the field used for the trigger.
Once that's working in Salesforce you can create a custom action in DayBack that will check that "send invitation" field, firing the same trigger. In DayBack that would appear as a new button on the event: a button you could name "Send Invitation". Basically, custom actions can set any field in your event or custom object, and then any triggers tied to those fields would fire.
You'll find notes about how to do this and a sample "make active" custom action here that you can use as your template: Custom Actions
Email Notifications in FileMaker
How can I add Email Notifications to my solution?
Email notifications aren't built into DayBack Online, but you can configure your FileMaker Server to send out email notifications; this is actually built into to DayBack for FileMaker. Learn more about it here: Email Notifications in DayBack for FileMaker.