tChess is one of the best chess apps available for the iPhone and iPad. The low-priced Lite version offers many of the features of tChess Pro, including an elegant interface and lots of in-game extras. (Both versions have variable difficulty settings, but tChess Lite taps out at a 1200 ELO rating, which "corresponds to a strong casual player but is weaker than an average chess club player.")
tChess Lite offers an excellent interface for chess learners, whether passing the device in two-player mode, or solo against the AI, with a clean, 2D board view that you can flip 180 degrees by touching a button in the toolbar. Small white dots show all legal moves for a given piece, and you can hit forward and back arrows to time-travel through previous moves. Best of all for beginners, a light bulb button will offer a hint, and you can review all your previous moves as a list. Captured pieces appear above the board, and extensive settings give you a lot of control over gameplay and appearance; you can even switch to a 3-D or faux wood board.
If you're a chess powerhouse, you'll want to check out the additional features in tChess Pro, not to mention several other solid chess apps, but tChess Lite is a great option for casual players looking to hone their game.