The Apple Watch has a heartbeat sensor, which the iPhone doesn't. Other than that, it's mostly an extension of the phone (so far).
The way I see it, the iPad is just an iPod Touch with a bigger screen. So, why would anyone buy an iPad, when the iPod Touch is cheaper and easier to carry in your pocket? Answer: Some of the things an iPod Touch can do would be easier with a larger display to work with. Some apps aren't worth developing for the small screen on the iPod Touch, but with the bigger screen, they become practical.
The Apple Watch is good for things that you could do on your iPhone, but probably wouldn't, because getting it out of your pocket to do them is not worth the trouble. If only the iPhone could be comfortably and stylishly strapped to the wrist!
Some people are looking for one single use case to justify spending $350+ on a wristwatch that mostly duplicates iPhone functionality. There may not be one. But as with the iPad, there are many use cases that in aggregate will make the Apple Watch an indispensable part of people's lives.