The "I'm Feeling Lucky" button takes you directly to the first web page Google returned for your query. You will not see the other search results at all. An "I'm Feeling Lucky" search means you spend less time searching for web pages and more time looking at them.
For example, to find the homepage for Stanford University, simply enter Stanford into the search field and click on the "I'm Feeling Lucky" button. Google takes you directly to "www.stanford.edu", the official homepage of Stanford University.