In days gone by a woman in childbirth was said to be in groaning. (For fairly obvious reasons.) In order to celebrate the infant’s arrival a special groaning cake would be baked. Depending on local tradition this would either be presented to the wife during her confinement to sustain her during her labour, or served to the inevitable wellwishers who would come to view the child, or taken by the wife on her way to being churched and presented to the first person she met.
Cf Groaning Chair, a chair used by mothers to receive visitors after a birth and Groaning Malt or Groaning Beer, and even Groaning Cheese.