Abandoned Carts is the feature which will send an email notification to a shopper if they populate items into a cart and then leave the site. Once the cart has been inactive long enough it will be marked as abandoned and an email will be generated.

The schedule job is kicked off by the syncs

The process that makes a cart abandoned happens after the email process. If the email process does not work the abandoned carts will fail
To set-up your Abandoned Cart:
Go to Admin, Index > Abandoned Carts > Settings

3 Tabs
I. General
II. Email
III. Schedule
I. General
Under the General tab, set whether or not you want to Request guests enter an email before checkout (should already be enabled)
Then set the number of days before a cart will be abandoned (auto-set to 7)
Next, you can choose whether a cart will be auto-deleted, after which point you can set the number of days before this will happen.
If you have 'Request guests enter email before checkout' enabled, you can choose to have users notified of abandoned carts.
The notification delay is auto-set to 0 so that a user is notified as soon as their cart is listed as abandoned. You can change this so there are additional days between being listed as abandoned and the notification being sent.
The 'Always notify user until the cart is empty' option allows you to choose whether a user is notified on a daily basis until their cart is emptied by them making the purchase, choosing to empty their cart, or the cart is auto-deleted. This is auto-set to 0 and would likely only be activated if there were only a handful of days between the initial notification and the time of cart deletion.
Finally, you can customize the abandoned cart email notification received by users in the 'Email body' field. There is a preset message, but this can be modified to better suit a client's needs.
Once the details are set to your specifications, click 'Save' at the bottom of the screen.
II. Email
Set up the email body in the custom text editor.
III. Schedule
Under the Schedule tab, you can choose on what days and at what time you would like the system to change the cart abandoned status and notify users.