Unbaby, or shredder, is the term used in the Republic of Gilead to describe infants that are suffering from birth defects or physical deformations. These die shortly after birth due to their defects. They are usually taken away to be disposed of. It's unknown what is done with Unbabies, though given that they are sometimes referred to as 'shredders', it is hinted that this could be the way they are disposed.
In the novel, Angela is an Unbaby.
Becka's family's Handmaid gave birth to an Unbaby without a brain.
Commander Judd's second and third wives die shortly after giving birth to Unbabies, including one with two heads lodged in the birth canal - Judd refused permission to operate as the fetus still had a heartbeat. His fifth wife, Shunammite, also had an Unbaby.