Just like Adsense for Content places targeted ads on your content pages, Adsense for Search places targeted ads on the results page of the search set in motion on your page.
You can use the standard Google search box on your site and the user can then search the web or even your site. When you feel more comfortable, you can change the look of the Google search box, essentially customizing it by changing the colors and using your logo.
The best thing about Google Adsense for Search is that you can track what your visitors are searching for. That is, if the search has two or more hits. Unique queries will not be tracked. But you can see the top 25 searches performed from your website by clicking on the Advance Report from the Reports tab and specifying a date range.