Deleting photos from an iPhone
You can definitely do it on the phone, but if you have a lot of photos, that could take a while.

Assuming you are on a Mac...

Connect your iPhone to your Mac and open Image Capture (in your Applications folder). Click on the iPhone in the device list and it will start building a list of all of your photos. Once it's done, you can select the photos you want to delete (Cmd-A to select all) and then click the delete button at the bottom of the window (looks like a red circle with a slash through it).