Granola is rolled oats, nuts and honey (sometimes with other ingredients added). It is basically baked and sweetened museli.
It was invented in the US in the late 19th century and the name was originally a trademark, however it is now a generic term (it is still a trademark in Australia). It was indeed an American thing, never really taking off in Europe, however it does seem to be starting to appear on UK supermarket shelves of late.
It comes with a bit of a health warning, it's seriously high in sugar and fat, Kellogg's Fruit and Nut granola has almost 4 times the fat by weight than oven chips!