Hi
The full range of features is available when Apple Watch and iPhone are connected via Bluetooth.
You don't necessarily need to have your iPhone on or immediately around you (within arm's reach, for example) for the devices to establish and maintain their Bluetooth connection. Normal Bluetooth range is around 33 feet / 10 meters (this will vary in practice due to wireless interference).
Whenever your watch can't connect to the iPhone via Bluetooth, it will attempt, as a fallback, to connect to a known, compatible Wi-Fi network. When instead connected to Wi-Fi, the watch also still offers a number of features, including receiving and sending messages via iMessage. If your carrier offers Wi-Fi Calling and it is supported on your plan and enabled on your iPhone, you can also use Apple Watch to make calls and (subject to carrier support) send and receive texts.
If your watch is unable to connect either via Bluetooth or Wi-Fi, it again still offers some - although fewer - features. Features that remain available in each case are detailed here:
How to use your Apple Watch without your iPhone nearby - Apple Support
For the best performance from your iPhone and Apple Watch, including the most power-efficient communication between them, Apple recommends keeping both Bluetooth and Wi-Fi permanently enabled on your iPhone.
More information:
About Bluetooth and Wi-Fi on Apple Watch - Apple Support
If your Apple Watch does not connect to your Wi-Fi network in the absence of a Bluetooth connection with your iPhone, then follow these steps:
If you have not yet done so, update your iPhone and Apple Watch to the latest software, starting with your iPhone:
Check that your home Wi-Fi network is compatible:
- Apple Watch can only connect to 802.11b/g/n 2.4GHz networks. It cannot connect to 5GHz Wi-Fi.
- Apple's recommended settings for Wi-Fi routers and access points are detailed here:
Make a note of your Wi-Fi network name, the type of encryption that it uses and your Wi-Fi password.
With your iPhone connected to the Wi-Fi network and with your Apple Watch close by and connected to your iPhone via Bluetooth:
- On your iPhone, go to: Settings > Wi-Fi.
- Tap on the "i" icon at the right hand side of your current Wi-Fi connection's entry.
- On the next screen, tap on Forget This Network - allow a few moments.
- Then, with a short pause in between, disable and re-enable Wi-Fi using the toggle at the top of the Wi-Fi screen.
Reconnect your iPhone to your Wi-Fi network:
- Ensure that you connect only to a 2.4GHz network.
- If you have a hidden network (ie the network name / SSID is not broadcast), choose to add the network via "Other", then enter the network name, encryption type and password.
After your iPhone has reconnected, allow a short time for the information to be shared to your watch.
Re-test your watch's ability to connect to the network by turning off Bluetooth on your iPhone and opening Control Centre on your watch (swipe up on the display when viewing the time on your watch):
More information:
About Bluetooth and Wi-Fi on Apple Watch - Apple Support