I can't delete a photo album on my iPhone5?

I connected my iPhone 5 to my MacBook Pro to try and transfer all my photos in my photo album to my laptop so I could delete all of them, but it didn't work, at all. For one, it didn't transfer any of my photos and it added 2 photo albums to my iPhone that I can't delete. They are titled "Photo Library" and "Last 12 Months" I don't know why I can't delete them and I can't delete any of the photos that are in the albums. If someone can please help me I'd appreciate it so so much! Please and thank you (:

Added (1). I'm not very good with computers and stuff lol but do I plug my phone into my computer and do that?

Copy the pics to your computer and open the album then *tap tap tap* the pics and click delete. Or plug in your phone and manually open DCIM and go through the pics. I go with the second method for my pics.