they give you access to their list by allowing you to submit your promotional messages to them and then sending them out to their subscribers. This way, you get to basically "rent" their subscribers for your offer. You pay them usually on the list size and quality, and later you can ask them to become "affiliates" where they only collect a percentage of sales (if you can convince them your offer does well).
the website i linked you to, DirectoryofEzines.com has lots of lists you can check out and find one suitable for your offer.
and if you aren't happy with the choices there, you can search for other Ezine Directories.