When used in conjunction with the aptly named WordPress.com Stats Helper plugin (not by Automattic), you can present the info on your public-facing pages, such as displaying ‘Popular Posts’ for example.
WP.com Stats isn’t new by any means, but with the latest release – v1.4 – the stats (appear to) have finally become time-localized (whereas before, it was set to UTC time) making the information that much more helpful.
Recorded stats include: number of pageviews, top viewed posts and pages, referral sources (i.e. where people clicked from to get to your site), search engine terms (used to find your posts/site), and links visitors clicked on your site.
Beyond the nifty admin dashboard which displays all this info for the last 48 hours, you can also see summaries for the last 7 Days/30 Days/Quarter/Year and All Time. More importantly, the plugin runs entirely on WP’s servers, thus preventing additional (unwanted) load (i.e. strain) on your personal hosting account.
Having a better understanding of all these statistics can really help you figure out what works and what doesn’t, at least in regards to content. As for site optimization, I still recommend using previously mentioned Google Analytics in conjunction with WP.com Stats to get the best overall picture of your site’s effectiveness and operation.