Have you checked out the live demo? That's how I found out how to use the software. It's awesome!
The "Initiate" function allows you to begin a chat with a visitor. Most often, visitors who have questions or need help will click the button to chat with you. However, there may be times you want to initiate the chat first.
For example, when you enter a store, it's always nice if someone who works there comes up and says "May I help you with anything?". This is what the initiate function is for. Since the software allows you to monitor where visitors are on your site, an example of how to use this feature is as follows:
Let's say you notice someone clicking back and forth between to pages containing similar items. This might indicate they're having trouble making up their mind which one to purchase. You would initiate a chat with them, and ask them if there's anything you can help them with, or say something like "I've noticed you browsing Celine Dion's Greatest Hits & Celine Dion's Live CD. May I help you make a choice between them or do you have any questions I can answer for you today?"
Hope this helps!