Short version:
- Open Messages on your iPhone or iPad, scroll to a picture/video you want to delete.
- Touch the picture/video (don’t press, just lightly touch) until a menu appears.
- Select More… from the menu
- Be sure your image has a check box to the left of it.
- Tap the trash can icon in the lower left to delete the image.
If you have some videos in your Messages timeline, this is a nice way to free up space. Remember, these deletes are permanent, so back up your phone before you go on a deleting rampage.
UPDATE: Even better way (H/T Mike Goril), open Messages, tap Details button in upper right corner, scroll down to ATTACHMENTS area, touch and hold individual images, tap Delete from the menu that appears.