The logbook contains a chronicle of everyone who has seen the bug, and where it has been. While most of that is recorded on the online logs, that information is often not easy to get to in the field. Not to mention it is cool to have a physical record of its journeys, like stamps in a passport.
You can keep up with this bugs travels here: TB8363
Note: previously I had the pleasure of helping release a similar travel bug called Tell Me A Story. That one (which I think it still an awesome idea) was meant to travel from cacher to cacher. This bug here is meant to travel the traditional way, from cache to cache. Both excellent takes on the idea of having a travel bug that tells its own story.