It's getting a feel at first for how people visit the site, what obscure search terms are used, where they go. Do the "visits" come from real browsers (are images and JS being loaded)? What bots are coming and can they navigate the site too?

Obviously this is not measurement by itself. At that company I wrote a suite of very detailed measurement tools, and we used commercial JS-based tools too (Nedstat, Urchin). My point though is you need to understand the logs first to even know what the tools are telling you.