Having tried the App out today it plays just like core set Dominion, with decent computer AI opponents and an option for online play. Unlike the free web version which also exists, it actually uses the official Dominion artwork, which makes it much more appealing visually. Downsides are that the interface could do with a polish and I have had it crash mid-game. But heck, its free.
Although popular, Dominion does take a little picking up due to the variety of ways of winning and the dramatic differences from game to game caused by the different setups available. So although there is a tutorial I do imagine the App will be pretty baffling to the newcomer. But if you're a board gamer and enjoy card or Euro games, you may well enjoy this medieval-themed combination if the two, which focuses on players each constructing themselves a deck of cards which represents their kingdom. It really is a clever game and well worth a look. And of course, buying the core set rather than just getting the App means you reward the creators of this fine game.