Operators can monitor either the customer or the visitor at real-time. ("Customer" is who has clicked-to-talk, and "Visitor" is just website browser.)
Operators may instantly see customer status, including IP address, location, interface language, current webpage, browser, OS, referring site, etc. And the current customer details will be shown at the right side of the chat box.
So to monitor visitors.
Which will help the operators to respond accordingly and focus on the best prospects.