The best app for editing photos depends on how much you are wanting to do with the photos. If you are just wanting to make very basic edits- eg. cropping, auto brightness and contrast, and set filters, you can do this quickly and easily on Instagram (although this is with a view to wanting to share the pictures afterwards).
If you are after something which offers more technical editing capabilities similar to that of, say, Adobe Photoshop on a "regular" computer, a program like Filterstorm may be more up your street.
This app offers a whole range of editing capabilities, and even allows you to import photos in RAW format. It's not free, though. You'll have to pay £2.39 for it, so if you don't need all of these extra functions, you may be better off with a simpler app, like Adobe Photoshop Express which is free, and has excellent reviews on iTunes.