An idiom most commonly used in America - used almost exclusively by women, to express an overwhelming desire to have children and become a mother. Although it's not something that all women go through, it is most commonly seen to occur between ages 23 through 35. This is something both single women and women in committed relationships can experience - partially due in part to maternal instinct and the so-called biological clock; social norms/expectations for a majority of women that in that age range; and on occasion also due to religious perspectives on family life.
Jane had been married for a little less than a year, but was already so baby hungry that she was buying up toddler's clothes whenever she saw them on sale. Babysitting for friends was the greatest way to work past it, until she and her husband are ready to have children.
Ashley was surprised to find that she was suddenly baby-hungry after years of swearing she'd never have kids, once she found out she was infertile.