- checking the time (obviously)
- sleep tracking
- high heart rate warnings
- sleep and heart rate trends over time
- reviewing notifications or declining calls without grabbing phone
None of these are "killer apps" but they're conveniences. I like having an accurate source of time that I don't have to pick something up for. I like being able to track my sleep schedule and duration over time. I like to know when my heart rate is high so I can take steps to quiet down. I don't use many of the other features, maybe some sparingly, but I've never really used the Watch for its apps anyway. And I think only the last feature on my list, maybe the last two, needs iPhone.
I've had to go without my Watch for the better part of half a year because it's refurbished and I've been trying to diagnose an Apple Developer Program enrollment issue, and Apple won't tell me which device was previously used so I have to rule out everything I didn't purchase brand new, etc., but I still constantly feel its absence. It's just a convenience but it was a welcome one.
Note that the Watch did previously require an iPhone for initial setup, but it does not anymore.