I have the same problem and read over 10 threads and finally found a cure. Hope to reply similar threads so that we don't suffer again.
My situation: I have transferred some "albums" from my computer to the iphone and then I can never delete those photos on Iphone or ITunes.
Solution:
1. Go to ITunes and Click the little phone icon just underneath the menu bar and next to "Music". (NOT the menu on the left where it says "Devices")
2. On the left, you should find "Settings" -> "Photos'. Then you should "Sync Photos" on the right, and see "Copy photos from: [folder you can select]
3. For the folder you can select, select an empty folder (no photos inside). Any empty folder would do
4. Click "Sync" at the bottom right.
5. After the sync is done, check your photos in the iphone. The albums you have added from computer should be gone by now.
Why am I posting the same answer in different threads:
I'm frustrated that the answers on these thread do not work and I hope the next person can avoid running around the website to solve this problem.
Cheers,
AHL
Read more below:
If you've plugged your iPhone or iPad into your computer in order to transfer existing photos via iTunes, these are the albums that you can not delete. If you want to delete them, or specific photos within them, you'll need to go through iTunes again. For example, if you want to delete select photos from an album, you'll need to delete them from the album on your computer and then apply sync changes in iTunes. If you want to remove an entire album, just uncheck it in iTunes and sync again.
http://www.imore.com/cant-delete-photo-albums-your-iphone-or-ipad-heres-why