As Android Wear has now switched over to LTE compatibility you can just leave your smartphone at home and do shopping or exercise freely. Initially this facility is only available with LG Watch Urbane second edition. All other smart watches are still connected to smartphone through Bluetooth or WiFi. That means you need to carry the smartphone with you too.
But in this new technology your watch shares a phone number with your phone, but you can leave the phone at home. Hopefully all future smartwatches will come with an LTE radio ready which would be an attractive preposition.