Prior to the release of iOS 7, you needed to tap each photo individually to select, then delete the batch - a very time-consuming and tedious proposition!
Starting in iOS 7.0, you can easily select a range of photos you want to delete, then tap the delete icon. This is a very big deal which can save literally hours of work in certain high-volume digital photography workflows.
For all delete methods listed below, please use with care. This is a one-way trip and will permanently delete the images contained within Photo.app. Deleted images are unrecoverable.
In Apple's Photos.app tap the Photos group from the bottom of the screen:
Go to the Collections group:
Tap on one of the photos in the Collections group you want to delete. You will now see a grouping of Moments, as shown below. Tap Select:
Now, tap Select to choose the entire moment group as your selection:
After tapping Select to choose all photos within a specific Moment, you should see all photos showing as being selected with a blue circle icon. Tap the trashcan icon to delete all the selected photos:
Photos.app will now delete all photos contained within that Moment, possibly hundreds or even thousands, with fewer than five screen taps. This is a huge improvement over prior iOS versions!
A word of warning: If you have iCloud turned on and are syncing photos via PhotoStream, photos which have the date and timestamp within the range of the "Moment" you're deleting will be deleted also. Be very careful when deleting photos via this method, as there is no undo, and photos could be deleted which you don't intend. Visually verify the selected photos to make sure you know what will be deleted before tapping the trashcan icon.