Jony Ive was recently interviewed by Vogue. This passage, in particular, seemed like a fine summary of the purpose of the Apple watch (emphasis mine):

All of this syncs with your iPhone, making the watch the wrist-bound control tower of your life in tech. Monitor your heart rate or your movement in general. Tap to have Siri take a message, or send a voice reply. Pay for drinks with your wrist (Apple Pay will be, yes, Apple Watch–compatible). With this product, Apple is moving from your desk and your pocket onto your person, your pulse point.