Im guessing you have your watch sitting on a table or something.
If thats the case and it turns on randomly that would be your phone sending a notification to the watch.
Now all you have to do is figure out what app is doing it.
Actually found that if I go into the "Connect" app on my phone and click "Moto 360", there is an option for "Tilt to wake screen" on or off. I turned it off because it was driving me crazy seeing it turn on randomly.