If you have a compatible Windows Phone 8.1-based smart phone, you can enable a feature that lets you double-tap your handset's screen to wake it up. This can often be much more convenient than the normal method for doing so, which requires you to pick up the phone and press the power button.
Here's why you want to enable this: If you ever leave your phone sitting on a desk, table or other surface and want to view the lock screen to see whether anything has happened—by glancing at the notifications—it can be inconvenient to have to pick up the device so you can press the power button.
But with double-tap to wake, you don't need to pick up the phone: You can just double-tap the screen and go from there. And even if some notification requires you to sign in and display an app, you still don't need to pick up the handset. You can do all of it by tapping the screen.
Here's a short, shaky-hand video showing how it works. (Hey, I was on a plane.)
The trick, of course, is that double-tap to wake is not available on all phones. You need Windows Phone 8.1, of course, and it works on virtually all 8.1-equipped Lumia handsets. But it is also starting to appear on non-Microsoft/Nokia devices, including the HTC One M8 for Windows.
To enable double-tap to wake, open Settings and navigate to Touch. (It's way down at the bottom with the other Lumia settings apps, usually. On the HTC One, you can find it in Motion Launch settings instead.)
Then, change the Wake up option to On.
That's it: You can now double tap the screen to wake up your phone more easily.
Note: Double-tap to wake and Glance are different functions and have no dependencies on each other. So you can use double-tap to wake on handsets that don't support Glance—like the Lumia 735—or you can use them together on phones that do support both.