Say I have a blog that talks about my web design service. Now if I discover that lots of people are searching for 'prices' through the site search option, I will get a signal that lots of people are interested to know what kind of prices I charge. If I make this aspect of my service clearer on my home page, I will be able to retain and may be convert more of my visitors into prospects.

An easy way to track this statistic is through Google Analytics. Yu should edit the site profile option and activate the site search option as shown in the picture here. Click on the 'Do track the site search' option and then enter 's' in the query string parameter. Save the settings and Google Analytics will now start tracking the site searches for your blog.

While this does not directly help in SEO of your blog, once you get to know which keywords people are using to land up on your blog, which search engines are sending you the traffic and other such information, you can make a plan to make suitable posts to serve these people.

I personally look at the bounce rate of the various pages on a high priority. If some pages have a high bounce rate, I check that to see if I can introduce some hooks to get people to stay longer on that page. You can add the related posts plugin to add some stickiness.

Don't forget that your home page may have a high bounce rate because the repeat visitors will just read your latest post and go away.