Deep sleep is when the baby sleeps soundly and doesn't wake up easily. Babies are less wiggly and don't make many of those cute baby noises while in deep sleep. Breathing and heart rates are typically more regular, too.
Light sleep is when a baby's brain collects and processes memories. So babies might wiggle or twitch a bit, and their eyes may move rapidly back and forth under closed eyelids (rapid-eye-movement sleep, or REM). The younger a baby is, the longer this light sleep stage lasts.
Active/Awake means that a baby is a bit more alert or is waking up. This can naturally happen as babies transition from one sleep stage to another. Babies are known to get a bit restless or fidgety before sleeping again.