IPhone – How to Permanently Delete Photos from iPhone

Presuming you're not looking to securely delete these photos, just recover space that they're consuming, as suggested by your original question, let's just start simply...

Aside from the suggestions by superriku11, including using iPhoto to transfer them off with the delete option and Image Capture, you do realize that you can, in Photos in your Camera Roll select Edit and then proceed to select a series of photos and then Delete them. This is time consuming for lots of photos, but does allow you directly on the iPhone to get rid of images you may no longer want to keep. This is the obvious solution to getting rid of multiple images at once but some people forget about it. Realize that if you delete a photo in the Camera Roll that's in an Album it goes away there too. You can delete albums using the Edit button, but this keeps images in the Camera Roll.

If you want to get rid of all the photos in your Camera Roll all at once, go into Settings > General > Usage under Storage click Photos & Camera and the right swipe Camera Roll to bring up a Delete button. Give it some time and it will delete all your photos in the Camera Roll. Likewise you could delete all the photos in your Photo Library and/or Photo Stream the same way.