The Borg baby was an infant girl that had been saved from the Borg by Seven of Nine in 2377 along with four other immature Borg drones. The other four were Mezoti, Icheb and twin brothers Azan and Rebi. The baby had been in a malfunctioning Borg maturation chamber when Seven saved it by transporting it to Voyager for medical care.
In the weeks after its rescue Seven took personal responsibility for its care and had begun raising it herself along with her wife captain Kathryn Janeway. Seven grew very attached to the baby girl and was actively including her in the plans for the couples future. Seven obviously wanted to raise the child as her and Janeways own child. Janeway stated that she would have loved to raise the baby with Seven but admitted to feeling that their dangerous lives and demanding positions on Voyager would have prevented them from giving her all the care she needed. Soon after, Voyager came into contact with the baby's people and located some of her relatives. Captain Janeway decided it was for the best if the baby girl was returned to her family, a decision that greatly upset Seven.
Seven accompanied Janeway in the Delta Flyer when they were returning the baby to her people. Janeway knew that Seven only went with them to try and find a flaw in the family that would take custody of the child so that she could use it to keep the baby herself. Janeway was not sure if she would have been able to stop her if she had found such a flaw in the family because in Ichebs case Sevens instincts had been completely correct. Unfortunately for Seven, she found no such flaw and was forced to give up the baby. The incident nearly drove a wedge between Seven and Janeway and caused a great deal of hurt between them. Janeway stuck to her decision that it had been in the best interest of the child but Seven disagreed, feeling as if her opinion did not matter to Janeway. In the end the couple decided to agree to disagree on the decision and to simply leave it in the past, otherwise it would hurt them and their relationship in the long run. (JB: "Just Between Fire & Ice")