Discovered by a reddit user this morning, the hidden trick works in any app that lets the iPhone's volume buttons be used to take a photograph. Examples include Snapchat, Camera+, and Manual, all apps where the iPhone's volume button works in the same way as a press on the on-screen photo capturing button.
To use the Apple Watch as a remote trigger, open a compatible app like Snapchat, open up the Music Glance, and turn the Digital Crown. The action will cause the camera to take a photograph, much like pressing on the iPhone's volume button would do. It also works within the Music app itself.
This seems to work because in the Music app and the Glance, the Digital Crown serves as a replacement for the iPhone's volume controls, triggering the camera functionality. Headphones with volume controls work in much the same way. It's not clear if this was an intentional feature addition or if it's a bug that was overlooked, but it's a handy way to use the Apple Watch as a shutter remote for iPhone apps that support the functionality.
Though the Apple Watch can be used as a remote trigger for compatible apps through the Music Glance, the function is not as feature rich as Apple's remote control option for the built-in camera. With the default camera, the Apple Watch can turn the iPhone on and capture a photograph.