Android Wear watches are pretty basic in their operation. You don't manage apps on them, or install widgets, or tweak permissions... all that stuff happens on your phone. Still, this is brand-new hardware and software, and sometimes things stop working properly. The Android Wear equivalent of "have you tried turning it off and on again?" is to perform a reset, restoring it to the factory default settings.
Don't worry, the apps all come from your phone, so after pairing it again using the Android Wear phone app, you'll be right back where you used to be.
Reseting your watch: A fix of last resort
It's quite easy to do. Just say "OK Google" or tap the watch face to bring up the voice prompt, then tap the red "G" circle in the upper right to bring up the menu. Scroll down to Settings.
The Settings menu holds lots of useful options, like screen brightness, always-on screen, airplane mode, and more.
Swipe down the list of options until you see Reset Device.
Choose that and you'll be prompted with an "Are you sure?" message. Select the checkbox and the watch will reset, returning to its out-of-the-box state after a couple minutes.
You'll have to re-sync the watch with the Android Wear app on your phone, select your preferred watch face again, and choose "resync apps" in settings on the Wear phone app. Resetting your device should be your last resort—the Restart option above it should be the first thing you try if your watch isn't working right.