What causes the green light on the back of the watch to come on?

Hi

The green LEDs are used by the heart rate sensor. It is normal for the sensor to take background measurements of your heart rate regularly throughout the day, but the LEDs do not remain permanently lit for this purpose.

It should not typically be possible to see the LEDs. For the best performance from your Apple Watch, check that you are wearing your watch sufficiently snugly on the top of your wrist.

Your heart rate. What it means, and where on Apple Watch you’ll find it. - Apple Support

Should you find that the LEDs are permanently lit, you may have a workout or other fitness-based session in progress (there may also be a runner icon on your watch face). In the Workout app - and also any third-party fitness tracking app that you may have installed - be sure to end any workout that is currently paused or in progress:

• Work out with your Apple Watch - Apple Support
• https://help.apple.com/watch/#/apd36e57e00c

If the icon remains / the LEDs remain lit up after ending any active workout, restart your watch:

Restart your Apple Watch - Apple Support

That is the heart rate monitor. It will be on if you are using the Activity app.