Deleting pictures from 'Photos' application

I am a iPhone newbie, got my first iPhone 6. I was playing with iTunes, I had connected my iphone to my PC. I clicked on the photos tab, on itunes, and clicked on Sync Photos. It basically transferred all my pictures from my PC to the iphone. I had thought it was going to be the other way around, but oh well, I am a newbie, right?

I clicked on Sync Photos to uncheck it, and it "deleted" all the albums that had been transferred from my PC to the iphone, BUT, when I click the photos app, all the pictures still appear arranged under a 'Years' screen. When I click on the pictures, I am taken to a 'Collections' screen. When I click on each picture, I am taken to a 'Moments' screen. I am able to click on 'Select' at the top right of the screen. This gives me the option of selection as many pictures as I want, I see the 'trash' icon at the bottom right corner, but it's grayed out, I am not able to delete the picture, or all the pictures, as a matter of fact.

I would like to delete these pictures if possible, could this be done?

My iOS software is up to date, I have iOS 8.3.

Thank you