I've been in the web dev game for a while and I have, on and off, tried Google Analytics... and, as newb as this may sound, I still haven't seen what usefulness comes from it. If anyone can provide insight and usages, please do so.
Personally, one of the things I use GA for is finding problem pages (pages that the visitor doesn't spend "enough" time on, meaning the page didn't satisfy them). Also, you can find new search phrases to target with new material.
mephisto absolutely right about keywords. i use most low frequent keywords to find the topic for new articles) sometimes it usefull to use "map overlay" if you want to target for specific region
Wow, there's a lot you're missing here then. Everything from the content on your site that people are looking at, to understanding dropoff points for important process flows within your site. These are all actionable areas that can help you improve your content and conversion rates.
Avoid google tools, such as analytics, like the plague - if you wan't more control of your seo. Maybe OK if you have something unique with no affiliate marketing - but google doesn't like affiliate marketers - so the less you let them find out about what you are doing, the better. Guru's such as Greg Jacobs (creator of Mage) advise this - and a number of users in my groups found that some of their sites bounced from a rank of over 100 back to the #1 spot on google within days of removing it. Use the open source Piwik instead. You will need to learn how to set up an SQL database on your server - fiddly but only takes a few minutes, then you control eveything. Why do you need it - TESTING. Particularly split testing. You should be testing everything you do online - then do more of what works and dump or improve what doesn't.
I'm just speaking in general terms for web sites. I guess it's something I need to study more and really learn the tricks of it. I have seen the keyword aspect, and I did find it useful. After posting this I started concentrating more on the main keyword getting me traffic and spreading it around as a backlink. The site I'm doing that with has had increased traffic today.
I found that some of the search terms people were getting to my page with were surprising. I had some interviews on my site that I had kind of forgotton about that were getting hits. Now I am redoing those pages to better take advantage of the traffic.