“Do Not Disturb” option, when enabled stops notifications from popping up on your Mac. This is quite useful when you're working on something, and need no hindrances. If you have the habit of downloading things at night, this feature is helpful, as the notifications pop up will not disturb your sleep.
In the earlier versions, you could easily enable “Do Not Disturb” option, by pulling down the notification center and choosing the toggle, “Do Not Disturb.” However, things change in OS X 10.10 Yosemite. The DND toggle might not be visible in the Notification Center but you can still enable it from elsewhere.
Here is How to Enable “Do Not Disturb” feature in your OS X Yosemite:
Step 2: Do see the changes – the notification tab will go pale instead of dark black. When it's pale (greyed out), it means Do Not Disturb is ON.
Step 3: To disable this feature, re-do the first step. Your notification tab will be back to dark black, indicating that “Do Not Disturb” feature is disabled.
Alternatively: Open the Notification Center (click on that icon) and then drag down (two-finger swipe). This will reveal the Do Not Disturb switch.
Mac running on OS X Yosemite may feature some of the changes like the one mentioned before. However, they will not be taken away totally; instead, there will be some changes.
The feature is kind of too subtle though. I hope that in the upcoming releases of Yosemite beta (or in the final version), Apple fixes this. We've seen that the Do Not Disturb feature sometimes doesn't work from the System Preferences → Notifications panel. Oddly disturbing, I'd say.