First and foremost, go to your home screen and open your Photos app.
At the bottom of the screen, you will click the "albums" tab. When the albums icon is blue, you have properly selected that tab.
Next, click "edit" in the upper right-hand corner of the screen.
After clicking edit, you will see that each album has a minus sign "-" in the upper left-hand corner of the album. Click the minus sign for the album you want to delete.
You will then see a prompt confirming that you are sure you want to delete this particular album. The photos will remain in your Photo Library, but you will no longer have a separate album. To confirm, click "delete album."
When you are done deleting the albums you no longer want, click done in the upper right-hand corner.
And, voila! You have deleted albums in your iPhone's Photo Library. See how easy that was?
Sometimes, when you are busy or out and about and your iPhone starts ringing, you don't want to pick it up, but you know it might be so-and-so with that important call you've been waiting on.