After you Get Online on your Live Chat, go to the Visitors tab and you will have an overview of all your current website visitors. By viewing the columns, you could know their info including: Name, Country, State, City, Email, Current Page, Where From, Current Page Browsing Time, Search Engine, Keywords, etc.
You can select a visitor you want to monitor and click Details link to view more information of the visitor, including: Navigation, History, Operating system, Browser, Time Zone, etc.
This is valuable information for sales lead spot, location focus, etc. For example, you may know which product is more popular if more visitors are from the specific page.
You can also manually Invite a visitor. For example, if you find a visitor is onsite for 5 minutes, you could invite him/her to chat with you, thus potentially boost your business.
Note: If you want to hide/display the columns or adjust their orders, you could click Preference in Agent Console then click Column under Live Chat. Moving the columns or changing the size in the Visitors tab is also available.