TRASIR shows you what connection data you're sharing with the world
Whenever your browser establishes a connection with a website, that website learns a great deal about you. It knows your current IP address (and thus your country and region), your browser (or what your browser claims to be – some browsers fake this), your OS (approximately), your language, etc. In short, it gathers quite a bit of data. Some of it is inferred, most of it is only somewhat accurate, and all of it can be faked if you know what you're doing and care enough to fake it.
TRASIR takes this information and exposes it to you in a very bare-bones layout; it spits out your IP address, host, country, region, and more. The site is free from any advertising, and I somehow get the feeling that it was made to look creepy. It almost looks like a screenshot from an early 90s sci-fi film (like something that a CIA spy would have used back then).
This sort of thing can be useful for explaining to your less-nerdy friends and family why you're so concerned with online privacy. It's interesting to access it under Private Browsing ("porn mode") in Chrome and Firefox, because you could then show whoever you're trying to educate how much information the site possesses about you once you access it, even if the local browser doesn't retain it.