Moto Assist
For setting the do-not-disturb sleep mode, driving mode (automatically read back texts and incoming calls), home mode (same sort of thing, so you don't have to always have your phone in your pocket or have to run to see who's calling), and a meeting mode that ties into your calendar so your phone won't bug you when you're busy.
Moto Actions
This uses the four IR ports on the front of the phone. You can wave to silence calls and alarms, and it looks for your approaching hand (or face or whatever) to turn on the display peek so you can see time and notifications without waking the entire phone.
The old "OK, Moto X" voice command prompt still works, but now you can get cute with it. "OK, NeckBeard" is absolutely an option.
Actions also controls the wrist-flick action for launching the camera app, a feature you don't realize how much you missed until you start using other phones without it.
Moto Voice
Motorola made talking to your phone cool with the original Moto X. And it's gotten better. You now can official set your own launch phrase. The old "OK, Moto X" still works just fine, but now you can get cute with it. "OK, NeckBeard" is absolutely an option. And like before, you can utter your launch phrase at any time — the phone doesn't actually have to be awake.
You also can now speak your PIN to unlock the phone, if that's what you're using (though Trusted Bluetooth devices are back, and we highly recommend that if you have a Bluetooth device nearby), and you can choose with voice commands work while the phone is locked.
Moto Display
Moto Display
This is the renamed Active Display. It's what lets you peek at the clock and notifications without having to hit the power button, and it's controlled form within the umbrella Moto app. You can chose whether you want to use it in the first place (it's on by default), choose which apps you want to appear in Moto Display (maybe it's not the best idea to have a Tinder notification show up while you're sitting next to the boss), and you can chose to hide notification details if you're using a screen lock.
Again, one of the important things here is that each of those features is able to be updated independently from the operating system. That means Motorola — and not the carriers — controls those updates.