These are the things you can do with your Apple Watch when it is not paired with an iPhone
For the Apple Watch to have its maximum functionality, it needs to be paired with an Apple iPhone 5 or higher. Those looking for a stand alone watch can check out the Samsung Gear S, which has a built-in 3G radio. The next-gen Apple Watch is rumored to be a stand alone model that won't require the user to pair it to an iPhone to make/take calls, browse the web and get notifications.
But let's say that you have the current Apple Watch strapped on your wrist and you have left your iPhone at home. What functions do you have on your timepiece? Consider that the watch uses a Bluetooth connection to pair with your iPhone. Without the phone, your watch will look for a Wi-Fi connection that is rather specific. It will need to find a 802.11b/g/n connection on a 2.4GHz band. The faster 5GHz band will not work and neither will a public Wi-Fi hotspot that requires you to sign in. And if you don't have your iPhone paired with your Apple Watch, you can only connect to Wi-Fi hotspots that you previously signed into with your phone.
Without your iPhone paired to your Apple Watch, you can still use the clock, stopwatch, alarm and timer. You can also used a synced playlist to listen to music. Using the activity app, you can track your standing, moving and exercises actions. Once your iPhone is back within range of your watch, it can sync with this new data. Without your iPhone paired to your Apple Watch, you can still display photos from a synced photo app and track your workouts using your watch. And you can still use Apple Pay without your iPhone by opening up the Apple Pay app when you are in range of the POS terminal.
Now, let's say that you do not have a Bluetooth connection between your Apple Watch and iPhone, but are sharing the same Wi-Fi network. Under those conditions, what can you do with your Apple Watch? Well, you can use iMessages to send and receive texts, share Digital Touch messages with other Apple Watch wearers, set reminders or check your calendar with Siri, and you can still check your email, weather, and calendars. You also will be able to access all native apps and most third party apps. You can also find your current location using Apple Maps.
While your Apple Watch works best with a Bluetooth connection to your iPhone, it is nice to know that there are some things that you can do without having that connection.