The first generation Motorola Moto G is now receiving the Android 5.0.2 software update. According to the manufacturer, the update brings Lock Screen notifications, the new Recent Apps menu, the Ambient Display which will show notifications even while the screen is off, and the new two-finger slide gesture that will reveal the Quick Settings menu from any page (and the new flashlight that is part of Quick Settings).
Other new features include the ability to have multiple-user sign-ins, a display showing the estimated time until the battery completely charges or discharges, and the 64-bit ART compiler that speeds up the opening of apps. Smart Lock allows you to use an Android Wear powered device (like a Motorola Moto 360 smartwatch) to unlock your handset.
While the size of the update wasn't listed, it is recommended that you connect to WiFi before installing the update, as such update files are usually large in size. Motorola also suggests that you ensure your battery is appropriately (at least 50%) charged before installing the update.
One last note. Since the update is being sent out on a staggered basis, you might not see it hit your device for a few days yet. There is no need to get upset. Just when you're about to send a strongly worded letter to Motorola and your carrier, the update will hit your Moto G.
source - Motorola | AndroidCentral