The development of this game will be an ongoing process. Once Leejunz is released, you'll be able to play it. Parallel to that, there will be public testing events every now and then, as announced on the blog (similar to this preview event, but open for everyone). The private testers will continue to test new content and its integration behind the curtain, before it hits open testing, and before it goes live. If more private testers are needed, the devs will have a look at the application forms, and choose suitable people from that pool. For everything else (= the actual game, the public testing events) you won't need to fill out that application.
Edit: Ninja'd.