When you search using the search widget in Safari it actually saves your searches. If you click on the magnifying glass in the search widget it'll show a list of the past searches. So if you are using someone else's computer and you don't want them to see what you've been searching for you might want to clear this list when you are done. You can clear the list of past searches by clicking on the same magnifying glass and selecting the "Clear Recent Searches" option which is shown beneath all of the list search terms.