It lets people browsing your bookshelf know whether a book is available for trade or not. "Available" means just that; it hasn't been released yet, you're finished reading it, and anyone can ask for it. "To be read" means you haven't gotten around to reading it yet; not yet available. "Traveling" means that it's been released or mailed to someone and is no longer available. "Permanant Collection" means that you liked the book so much that you're keeping it and have no plans to release it.

"how do you let the site know, once it's registered, where and when you did so."

Once you register a book, the date it was registered and your location appear alongside it on your bookshelf. If you registered the book somewhere other than where you live, you can mention that in the comments. When you release a book, you get the option to document that place and time as well.

Hope this helps.