Hi
The green LEDs are used by the heart rate sensor. It is normal for the sensor to take measurements continuously during workouts, but they should not otherwise remain permanently lit.
If the LEDs are permanently lit, then you may have a workout or other fitness-based session (via a third-party app) 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:
If the LEDs remain lit after ending any active workout, then it may help to close certain apps and then to restart (normally) both your iPhone and your Apple Watch:
Also be sure to use your Apple Watch in accordance with Apple's handling guidelines in respect of operating temperatures:
Keep Apple Watch within acceptable operating temperatures - Apple Support
If the issue persists or recurs, then it may help to unpair and re-pair your Apple Watch:
If the issue then still persists or recurs, then your Apple Watch may require service. I suggest that you contact Apple Support (remote diagnostics and/or mail-in service may be available, if required), make a Genius Bar reservation or visit an Apple Authorised Service Provider for assistance: