All the details needed is in the title. Albums not created on the phone cant be deleted from the phone.
"Folders" and "Albums" mean very different things to most people, and your original post gave zero indication that you were referring to photo albums.
I don't believe you can delete photo albums on the phone that are synced down to the phone from iTunes from the interface on the phone. You can go to iTunes and select which albums to sync by changing the option to just sync selected albums.