It appears that the new service will be similar to Netflix's streaming (which does not support the Mac, though they have promised it a long time ago) in that you'll be able to watch 40,000 movies and television shows in your browser. Unlike Netflix, however, the content will be priced individually with no subscription options. The video will be streamed with Flash 9.
Unfortunately, the program is still in beta and Amazon apparently has enough testers at the moment. However, you can sign up for their beta mailing list if you want to get in the next time they issue invitations.