Apple Watch users are definitely going to need a way to quiet their wearable device throughout the day. One way is to adjust the Ringer and Alert Sounds under the Sounds & Haptics section of the Settings of your Watch, or you can put it in Do Not Disturb Mode. Here's how:
To put only your Apple Watch in Do Not Disturb mode, open the Settings and navigate to Do Not Disturb. From here you can enable the Do Not Disturb feature. A crescent moon 
icon will appear at the top of your screen when your Watch is in Do Not Disturb mode.
To put both your iPhone and Apple Watch in Do Not Disturb mode, open the Apple Watch app on your iPhone and tap My Watch, and turn on Do Not Disturb > Mirror iPhone. Now both devices will slip in to Do Not Disturb mode when you enable it on the other device. This also allows you to schedule a time for your iPhone and Watch to enter Do Not Disturb mode by using the Scheduled slider on your iPhone.