If you're running iOS 7 or above, do the following:
1. Initiate the Photos app
2. Tap on "Albums" in the bottom right corner of the screen.
3. Tap on "Edit" in the upper right corner.
4. Tap the RED circle in front of the album you want to delete.
5. Select "Delete"
6. Confirm that you war to "Delete Album" at the bottom of the screen.