When you watch something, you observe it or guard it — like when you watch the latest episode of your favorite television show or when you watch your baby cousin.
You use the word watch (rather than look) when you'll be observing for a while, and with some care. If you agree to watch your neighbor's puppy, it means that you've promised to observe him carefully and make sure he doesn't get into trouble. When watch is a noun, it is the timepiece you wear on your wrist. Many people use their cell phones to get the time of day, instead of their watches.