If you try to smooth things over with someone by giving them a gift, you can call it a peace offering. After fighting with your brother, you might take him out for ice cream as a peace offering.
An attempt to pacify or mollify a heated situation sometimes includes a kind gesture or even a present — a peace offering. When you hurt someone's feelings or offend them, a peace offering can go a long way toward burying the hatchet. The phrase originally had a religious meaning and is found in the Hebrew Bible, where it refers to a gift of thanks offered to God.