When Apple announced iOS 12, it showed off improvements to notifications and Do Not Disturb. Primarily, notifications are now combined if sent by the same app, and users can revoke an app's notification privileges directly from the lock screen.
One of the biggest improvements to alerts on watchOS 5 is that alerts from the same app are now grouped together. Instead of listing each alert individually, one card is displayed per app, and if there are more alerts, you can see the silhouette of more alerts underneath — much like a stack of paper. Tap on the top alert to ungroup the alerts and view them individually.
Delivery quietly, or not at all
When viewing your list of alerts, swipe to the left on an individual alert. You can clear that specific alert with a tap on the "X," or view new options by selecting the three-dot button.
Select whether you want that apps' alerts to be delivered quietly, or not at all. Deliver Quietly just means that the alerts will still show up in notification center on your watch, however, you won't receive an alert that there's a new notification.
Selecting Turn Off on Apple Watch does just want it says — stops the app from sending any alerts to your wrist.
Do Not Disturb
Apple also updated Do Not Disturb mode in iOS 12, and one of those new features has spilled over to the Apple Watch. Specifically, whenever you manually enable DND from Control Center (swipe up from the bottom of the screen when viewing your watchface), you're given the option to set DND to stay on until you turn it off, expire in an hour, later that evening, when you leave your current location.