If you wrote something embarrassing, there is a good chance it is a Status Update. Let's check. First, we need to go to your Profile. To do this, click your name at the top of the page (pictured below).
Your Profile page should load up on the screen. Scroll down to find the status you want to delete and click the downward arrow in the top-right corner of the Status Update (pictured below).
Click Delete from the list of options there. Boom, done!