Perhaps you uploaded a photo a year ago, and you would like to have it remain on Facebook privately; while you should keep in mind that this picture has been on the internet and therefore can’t be taken back, you can change your privacy settings on that individual picture.
Simply click on the picture, so that you get this screen:
Then, click on the picture of faces with the drop-down arrow:
which will show a drop-down menu when clicked:
select Only Me and you should have a now-private image!