This is a new feature, inside the activity log. In the past you couldn't view your searches.
As far as I know, the only way to remove a search from the activity log is manually removing each search.
I know no one else can see my private activity log, which contains my past searches - I can only view them by checking the "Include Only Me activity" box:
but since I log in to my account on a shared computer and sometimes leave Facebook open, I am afraid someone will be able to see my past searches.
I have to find a way to delete all of my searches in the activity log. Is that possible somehow?