What com.apple.diskspaced service does?
I think this service check your available  disk space. 
If you have less than N% (~5%) of your HDD it will show a notification.

Until macOS Sierra this notification could be silenced by selecting (Don't show this again) but on macOS Sierra you no longer have this option.

I have 2% left on my HDD and I had to manually remove (Activity Monitor -> Quit) this daemon so I don't get this annoying notification.

I have searched for a decent way to stop this notification but I think there is only this solution.

Hope this help.