When you click on a link in our results page, your search terms are not sent to the site that you click on, which can be the case on other search engines due to something called HTTP "referers".
On modern browsers we accomplish this by adding a small piece of code to our page called Meta referrer. Some browsers (especially older ones) do not support this standard, however. For those browsers, and also in situations where meta referrer doesn't work, we send the request back to our servers to remove search terms. This redirect goes through r.duckduckgo.com.
You can disable this privacy feature. To do that, go to the settings page, select Privacy, and change the option Redirect to Off.
You also go through a duckduckgo.com redirect when you use a bang. That's simply because we need to know where to send you.
Prior versions on GitHub.