Watching a Community means that any public posts that are posted to the Community will be added to your Friends Page, where you can view them, but any private entry to the community will be blocked. Private means that the person who posted has blocked anyone who's not a member from seeing their post, so you'll have to join to see any private posts.
It's the same with any personal LJ. You can set your journal so that only the people on your friends list can see your entries, meaning that you will have to add this person to your friends list, and have them add you in return for you to see their private entries. You can also choose to have some entries, like art or fic, for example, open to the public, while keeping the rest of your entries private.