The new Merchant case is a protective case which is currently only available for the iPhone 5/5S. It is made of silicon and is designed to work with the Square reader. It protects your phone from small drops and scratches like most cases should, but also has a molded space on the back to hold the reader while it's not in use. It also has a slot on the bottom of the case to help make sliding cards easier.
The $20 case does protrude out the bottom of the phone significantly so docking would most likely not be possible, and plugging in the lighting connector may be quite difficult. Since the reader itself uses the headphone jack, that wont be obstructed at all, unless the reader is plugged in (obviously).
This case is the first of the "Works with Square" program and we will continue to see more of these while Square grows. Square is currently available in 3 countries - Canada, United States, Japan - and has just recently passed $16 billion in mobile payments.