If you'd like to remove something from your watch history you can do so by clicking on the "Watch History" button from the home page
Once you're in the Watch History section of your account you'll see all that you've watched along with the option to edit, notated in the upper right corner.
Click on the pencil next to "Edit" and you'll see a red box appear in the upper right corner of all the videos you've watched. Click the red X on any videos you'd like to remove from your Watch History and once you're done hit the check mark next to the word "Done".
Any videos you selected to remove will no longer show up in your Watch History section.