Indie rock is a subgenre of the alternative rock genre is used to term rock groups that are signed to independent lables.
Indie Rock is just short for Independent Rock and is not associated with any particular country. It is most predominant though in the US and UK.
There is no definate style to the music either and is just alternative rock to alternative country to Post Punk and Garage Rock.
Prominate Indie bands that you may have heard or should take a look at are:
White Stripes, The Strokes, Eagles of Death Metal, The Hives, Muse, Franz Ferdinand, Arctic Monkeys, The Libertines, Dirty Pretty Things, Babyshambles, and Razorlight.