This is variable for different sites.
Some sites will want to take a small percentage of the booking price for any bookings they bring to your business, or a fixed fee per enquiry, or perhaps a per-monthly fee for embedding your booking widget in their site. Others, of course, may offer embedding for free.
Often advertising comes at a cost, but the benefit for you is increased exposure and convenience for your customers. The benefit for them is a bit of revenue. But don't worry, if any site has a cost associated it will be clearly explained and you'll be able to opt out or cancel at any time.