When a person, typically a thin one, indulges in a large amount of food which makes their stomach stick out from the fullness as if they're pregnant.
In the movie Juno:
Juno: I'm pregnant.
Leah: What? Honest to blog?
Juno: Yeah. Yeah, it's Bleekers.
Leah: It's probably just a food baby. Did you have a big lunch?
Juno: No, this is not a food baby all right?