First, user have to ensure that LodgeiT is connected to QBO.  

The function of "Automatically synchronize clients" box is to enable the option of "Sync client details with accounting system" whenever a user will add a client.

Set this via gear wheel > settings, and press "import" 

Below snip shows that "Automatically synchronize clients" is currently ticked, and it will show up under "New client" page.(ie if turned-off, sync option under "New client" page will not be visible)

Click HERE, to learn more about on how to bulk sync LodgeiT client to QBOA

If it is an initial setup there is a tickbox to select ALL clients to import from QBOA to LodgeiT.

Note: If you want to sync customers from QBOA, please use Client Sync, but it will just sync contact details, address, email address.  In order to import financial you must connect QBO files one by one for each client 

Other related article:

QBO Client Sync - Import

Synchronise Client Details from LodgeiT to QBO