You can not delete individual photos from the PhotoStream. All you can do is reset it, deleting all the photos.
To reset the PhotoStream visit iCloud.com on a computer. If you do not see all the app icons (Mail, Contacts, Calendar, etc), click on the cloud icon at the top left of whatever app you are viewing. On the app view page click on your name at the top right, then choose Advanced and Reset PhotoStream in the popup.