The search results page retrieves some content from s3.amazonaws.com. The http referer in those requests contains the search term. Thus, even though duckduckgo.

The search results page retrieves some content from s3.amazonaws.com. The http referer in those requests contains the search term. Thus, even though duckduckgo.com doesn't know you performed a search, amazonaws.com knows your IP address, what you searched for, and when you searched for it. They probably have a log of all that information too.