PicsArt Photo Studio is a popular, feature-rich photo editor that was formerly for Android phones only, but it's now available for iPhone.
There are several apps that let you add effects and edit your photos, but PicsArt Photo Studio does those things and quite a lot more. In fact this app has so many features it can get a little overwhelming -- particularly with the number of interface elements on the screen.
Like most photo effects apps, you can snap a new picture or pull one from your photo library. With an image onscreen, you can use the buttons on the bottom of the interface to play with the main features of the app. A tools button lets you do things like crop, rotate, and resize the image, with extra tools including one that lets you crop to a specific shape. You have another button for effects with several categories such as Artistic, Paper effects, ColorSplash, and simple color corrections. From there you can use the drawing button to draw on your image with a fully customizable paintbrush, add text, add shapes, and even overlay another photo on top of your original image. Next you can throw a mask on your image and add a frame. Finally, an Add button lets you add things like clip art, callouts, more frames, and text. Frankly, the number of things you can do with your images is exhaustive.