To eat something very quickly and eagerly. A noun or pronoun can be used between "gobble" and "down." Now that the baby is eating solid food, she just gobbles down anything we put in front of her.
gobble something down
to eat something very fast, swallowing large chunks. The dog gobbled the meat down in seconds.The cat gobbled down the sardines.
gobble down
v.
To eat something completely and in haste, especially by swallowing large amounts at a time: The family gobbled down the peach pie. I was so hungry that when they gave me food, I gobbled it down.