There are multiple definitions - click on the translation that matches your context.
concerning a country or place that someone has chosen as their permanent place of residence
He was born in England, but France is his adoptive country.
in a particular relationship following adoption (=the act of taking legal responsibility for another person's natural child on the same grounds as if it was your own child)
Fourteen-year-old Fred would love to have an adoptive family with whom to share vacations and other activities.