Quick Smart Twitter Search is the claim that they make. It's an interesting engine, but it's really designed to follow the tweets of individuals, rather than Twitter as a whole. However, it really does provide a mine of information once you have found the person that you're interested in. Put in the Twitter user name that you want to explore and then wait for a while. There's a very irritating flickering while Gwittr goes and collects data and brings it back - this was a major weakness of the engine IMO - quite slow, and I was searching my name and I don't have a huge number of tweets. In fact, thanks to Gwittr I can tell you exactly: 1394 since February 2013. I can also tell you my top shared sites (bit.ly, which isn't helpful), top users that I mention, most used hashtags.
Thanks to the statistics section of the results I can also tell you that of 3231 tweets since December 2011 (an annoying inconsistency in dates there!) I tweet most on a Thursday, and between mid day and 1 o'clock. The earliest I've tweeted is at 5am, and the latest at 2am. (Not the same day I hasten to add!) I have tweeted 21 photographs, and they are all collected together, and I have linked to just over 1,000 webpages.
Gwittr is a useful search engine - it really pulls personal content together very nicely, and it's a great addition to your Twitter search armoury.