Union (U.S. $1.99) is a very well thought out tool that brings Photoshop-type power to your iPad or iPhone. It's the most impressive image blending app I've used, and it works wonders to help you create unique and compelling images.
When using the app, you first load in a background image, for example a landscape photo. Then, you add a foreground image that you want to transplant on top of the background. In the next step, you enter the mask layer by choosing the Magic Wand tool, which allows you to easily remove everything but the person.
The tool removes parts of the image based on similarity in backgrounds and luminance, so it is a lot easier if the background behind the person is more solid in color rather than patterned. If the Magic Wand tool doesn't do the trick, you can manually draw out the parts that don't automatically go away.
Union allows you to let your imagination run wild as you are not limited to only superimposing images. You can make the layers transparent, create double exposures, and more. The app also has extensive undo-redo commands, so you can just step backwards if you don't like what you've created.
Union for iOS
The app contains tutorial videos, which are much nicer than static help pages. Photos can be exported to your camera roll, Facebook, Twitter, Instagram or via email.
While excellent, the app suffers from a problem that is common among this type of app -- when removing the background, your finger covers the drawing tool, making it tricky to accurately remove an element. Some apps offset the tool from where your finger meets the screen, making the job a lot easier.
Despite this limitation, I was able to manage with the removal tool and created some great shots with little effort. Union is a universal app. It requires iOS 7 or later, and it is optimized for the iPhone 5. Give it a try if you want to create some unique and eye-catching compositions.