The Finnish boxes are filled with gender-neutral clothes (including outdoor clothes), diapers, toys, and more, to guarantee that all new parents have the basic necessities. A small mattress, sheets, and blankets also come inside the box so that it can double as a safe place for the baby to sleep if necessary (similar to a bassinet).
According to the BBC, "It's a tradition that dates back to the 1930s and it's designed to give all children in Finland, no matter what background they're from, an equal start in life. ... Many children, from all social backgrounds, have their first naps within the safety of the box's four cardboard walls."