It has been said to be named after a Clint Eastwood line in the movie Dirty Harry. “Do you feel lucky, punk? Well, do you?” However, I can promise you there is absolutely no connection with these two.
The “I’m Feeling Lucky” button on the Google search page was designed to save people time. It does this by taking you directly to the first web page that returns for your query. If you were to type in a keyword or keyword phrase in Google and press the search button, Google returns a results page that shows multiple websites matching your search phrase.
However, if you type the same keyword phrase in Google and then select the “I’m Feeling Lucky” button, the search engine skips the search results page and goes directly to the first ranked page for that search phrase. For example, if you enter the keyword “baseball” and click the “I’m Feeling Lucky” button, Google will send you to the home page of Major League Baseball.
So the “I’m Feeling Lucky” button is handy if you’re fairly confident that the first result in the search engine is going to be exactly the page you want to find. It saves you time and energy by taking you directly to what they hope you’re looking for.