The quick version of this is a legal book would be licensed, regulated and monitored under a gaming control board (state by state) in a state that allows for sports betting. An illegal book wouldn't be licensed and fall under those regulations or would be operating/taking money in a state that doesn't allow for betting. These illegal books are usually operated outside of the country's borders, like offshore. We have a great industry news page on Covers that gets into all the ins and outs of this.