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? 
How can I remove all my searches from the new Activity Log in Facebook?
facebook;privacy
Go to facebook.com/{your username goes here}/allactivity  click on MORE just under Photos & Likes, on the left side column  click on Search  click on Clear Searches on top.