What phone? What kind of movement - wave a hand over the screen or pick up/nudge the phone? What OS is on your phone? What update did you install?
Generalization here - likely Ambient Display, part of Lollipop and Marshmallow, it's in the Display section in Settings.
A little more directed - Motorola phones have the Moto app, within which is the Display section, you can enable those features there.