There are different methods you can use for the delete and it will depend on the type of video that you want to discard. For a video synced from iTunes you tap on it and select the delete option and this should work. If it is a recorded video, you tap on photos and open the camera roll and then tap on the specific video and then the trash icon. You then tap on the delete function and it should be removed from your device. For multiple recorded videos you open the photos application and open camera roll and select the video in question and then the delete option.