Archiver's Memory Lab uses an online cloud storage system to back up your images and allows you to order prints directly from the company. There are similar apps from other companies, including those that may offer local printing and delivery in your area, but this is nonetheless a decent, well executed app with quick response and upload times.
When you first open Archiver's Memory Lab, you'll be tasked with first creating a user account so you can start uploading your images. From there, you can upload any images from your photo library to an online account and then save them there or order prints of those images. This is a very fast process -- working in just seconds and allowing you to pull images from any of your connected photo albums with a few quick taps. The app doesn't allow you to organize or edit the storage of those images once they are uploaded, but the speed more than makes up for these limitations.
If you want to order prints, save images in the cloud for later access, or just ensure there are a few online you can access from another device, Archiver's Memory Lab is a decent app. It's not the most advanced or feature-rich photo storage solution for your iOS device, but it is free and relatively easy to use.