Unless I'm missing something, it doesn't look like there's a Reminders.app for Apple Watch. From what I've seen, Apple Watch will let users set new reminders via Siri, but there doesn't appear to be a way to actually view those reminders in list form on the Watch.
So, for instance, you could say, "Siri, remind me to turn off the oven at 6 PM" and at 6 PM Apple Watch will alert you to turn off the oven. My guess is these reminders will also sync to the Reminders.app on your other iOS devices where you could also view them. But there's no central place on the Watch to view all of your upcoming reminders.
Now it could just be that Apple felt it wasn't practical to display a list of reminders on a small screen. But it also raises an interesting question about the "correct use" of Reminders.app. I tend to use the Reminders.app on my iOS devices both to set reminders, like in the example above, but also to store simple shopping lists, like grocery store and drug store lists.
Since the Apple Watch announcement, I've imagined how convenient it would be to display shopping lists on my wrist so that I could have both hands free while in the store.
But maybe Apple sees this use as the "wrong" way to use the app. Maybe it's literally just meant to be used for reminders and using the app for list making is "off use."