Yes, the Apple watch works without an iPhone, but features will be limited. Here's which feature you can use and which not.
You will see a red icon with a diagonal slash through the middle. This indicates that the Apple Watch is not currently connected to an iPhone.
You will have more access to functions if you're running the latest watchOS or if you are using a cellular model. You can make and receive calls, send texts, emails.
If you have only Wi-Fi available, then you can still be able to use some apps. Such as receive iMessages, use Siri, listen to music, and use any apps that work with Wi-Fi.
if you do have not access to wifi then you can use music or podcasts that have been previously downloaded to your Apple Watch, you can still listen to them.
Also, You can monitor your heart rate, and your activity, and set any alarms and timers on your Apple Watch.
And the great thing is that You can also use Apple Pay without Wi-Fi. Which is very useful if you forget your iPhone.