A bottom baby is a baby that was conceived via anal sex. Although highly unlikely, it is possible for a sperm to reach the egg while a couple is having anal sex. For example, if the male pulls out when he cums, and unloads all over the females arsehole, some sperm can get into the vulva and thus a bottom baby is created.
If a person ever finds out that they are a bottom baby it is devastating to that person.
Jack: "Hey what's wrong with Andrew, he seems a little down?"
Phil: "Oh he just found out that he's a bottom baby"
Jack: "Poor guy, he must be devastated"