It means you won't be able to see the member's name when you view the listing. You'll still be able to contact them, but you'll have to use DealStream's messaging system.
People list anonymously because they want to screen responses. But the downside is they get a lot fewer responses.
If you respond to an anonymous listing and you get a reply, the reply will show the name of the member who created the listing. In other words, the member who created the listing will no longer be anonymous.