As you can see, an abandoned order is simply an order that a visitor decides for x or y reason not to finalize their purchase after having added one or more items to their cart. 
The "Abandoned Order" add-on allows you to take action to recover these orders with dedicated emails or push notifications.

From the list of abandoned orders you can send an email, a push notification, or both, to encourage clients to finalize their order. The message templates associated with these actions are of course customizable (and it’s highly recommended).

The subject of the reminder 

Whether you decide to send an email or a push notification you'll have to take care of the subject of your message :it’s a major criterion on the opening or not of your reminder message.
Here are some tips:

• Personalize the subject of your message according to your client (add their name for example)
• Refer to at least one product in their shopping cart. This technique is a little more time consuming but it can pay off.

The content of the reminder

After the subject line comes the content of your message. These tips apply more to follow-up emails than to push notifications (which are much shorter than an email):

• Recap their cart, showing the list of products as well as the order price.
• A button that clearly redirects your client to their cart 

The timing

Finally, choose the right timing to send your reminders. Unfortunately, there are no fixed rules for deciding the best time. 
Some people send out reminders very quickly while others wait several days. Use the information available in your back office to define the best time to send your reminder(s). Study the frequency of purchase of each client, the amount of their cart, etc.

Experience will help you understand your clients better and find the right time to notify them.