It is basically a web stats application. You know, the ones that show you who your visitors are, where are they coming from, which pages they visit, etc. It also gives statistics for commerce sites to track conversion rates, which has so far not been very useful to me. Nevertheless, I jumped on and gave it a try.
And it wasn't me who is suffering alone -- searching through Google Blog Search sees rants from everywhere. Google Analytics has to be one of few products that came out from Google without a "beta" tag on, but maybe that's how Google denoted their alpha-quality software :)
12 24 36 hours.
Now, if only Google can provide better statistics for our AdSense pages...