When you create or edit a task if you set ‘Send Notification for this Task’ to Yes - see below - a notification will be emailed to the person the task is assigned to.
The notification email which will contain the details of the task that has been assigned, together with an invite file which optionally allows people to add the notification to their calendar.
How you work with the notification received will depend upon what the task is, the calendar or task list you use and how you like to organise your tasks - for example you may decide to add a task in Outlook or add an event to your calendar. Check the help for email client or calendar you use for information about adding tasks or events.
When you open an existing task you see any details of the last notification sent - see below - you can resend the notification by setting ‘Send Notification for this Task’ to Yes and saving.
If you get this error message or something similiar - "Activity Saved but an error occurred sending the notification" and one under the task itself saying "Problem sending task notification to xxxxxxx on 23 May 2017 by aaaa bbbbbb Error - Mailbox unavailable. The server response was: 5.7.1 Client does not have permissions to send as this sender".
it maybe the following issue
The error means there is a problem with the connection between Donorfy and your email system see this for more info Troubleshooting Problems Sending Emails
It can be difficult to get some 'on premises' email systems - like Microsoft Exchange - to work well with other systems like Donorfy. Some people have circumvented that problem by setting up a gmail account for sending Donorfy emails see this Using Gmail with Donorfy