Recent Searches are the list of the last five searches that are performed by the individual visitor in a 30 day period. Recent Searches are displayed above the Pinned and Popular Searches. The below screenshot is from a demo Magento store - The Recent Searches are displayed with a small icon of a clock in front of it.
Recent Searches expire after the cache memory is cleared from the browser. They can also be individually deleted by the user, by clicking on the 'X' button on the right side of the Search Suggestions window.