Part of their idea is just making U.S. banknotes easier to handle. To that end, each bill has its own color for simple identification. They also come in different lengths -- the dollar’s the shortest and the hundred’s the longest (see up top) -- so that when you stack your bills, you can instantly eyeball how much you’ve got. Varying the size is especially useful to help blind people distinguish between notes.
Perhaps most dramatically, the bills are arranged lengthwise. Dowling Duncan say they conducted extensive research on how people deal money and discovered that transactions are almost always carried out vertically. It's true: How often do you hand someone a bill clutching the center widthwise? How many money machines accept cash horizontally? The new orientation would obviously take some getting used to, but in Dowling Duncan’s view, it’s ultimately more instinctual.