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)

Visit this article to learn more about Client Sync (QBO to/from LodgeiT)

Note: If you want to Client Sync (QBO to/from LodgeiT) use that guide, 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 articles:

Synchronise Client Details from LodgeiT to QBO

Contact Details Mapping (LodgeiT > QBO)