Remember like a year ago when Google was going to add notification syncing to Play Services so you wouldn't have to see the same notifications on your phone and tablet? That still hasn't actually been rolled out, but the new Pushbullet v14.1 does pretty much the same thing. By expanding the notification mirroring service, Pushbullet can sync notifications across all your devices.
As an example – let's say you get a phone call, but you've got a tablet in your hands. Pushbullet will automatically mirror that notification from the phone on your tablet so you know who's calling without picking up the phone. If an app produces a notification on your tablet, and you swipe it away, it is also cleared on your phone (and computer, if you have the Pushbullet extension). You can also see the content of text messages on a tablet with Pushbullet's new notification sync.
Syncing the dismissal of notifications is probably the coolest part. No more will you have to see the same things when you pick up a different device. Cool though it is, the developers are careful to point out this is a beta feature. It can be enabled in the settings of each device you want synced, but watch for bugs.