I'm not sure I can explain it well enough, but what the iPad *does* is nearly everything (with some limitations). I think Steve Jobs used the "truck and sports car" analogy (meaning regular full-featured computers like desktops and notebooks were "trucks" and lighter-use devices that cover all the basics were "sports cars"), and he said that while trucks are great and handy, not everyone actually needs one. In fact, even truck owners would probably admit that 90 percent of the time what they do with their truck could be done just as well in a car or even lighter vehicle.
So really what the iPad has done is taken an approach to computing that removes almost ALL of the obstacles people had to using one well (complicated file system, maintenance, organizing, etc) and give you a lightweight, runs-all-day, go-anywhere system that doesn't give you any crap, and specializes in consuming content, which is what MOST people do MOST of the time with computers.
An iPad can be used to productivity as well, but it's not really the focus of the device. It's primarily designed for what I would call "casual computing" which covers e-mail (short replies), reading/surfing, Facebook et al, games, videos, music, viewing photos, ebook reading and other "easy stuff" that people like to do. That said, corporations and other businesses have been incredibly innovating in finding ways to make the iPad work for them as well.
By putting all that into a fun and incredibly elegant package, it makes computing fun and enjoyable for people who otherwise have difficulty with "regular" computers and also gives us a further sense of "freedom" beyond what notebooks do. For us "power nerds" who are perfectly comfortable with computers, it's still a remarkably enjoyable device that, like the iPhone or iPod Touch, allows us to bring most (but not all) of our computing tasks with us everywhere we go.