If a society is classless, people are not cut into layers such as upper class, middle class, and working class — no group sitting above another because of money, birth, or job. Politicians and writers use the word when they talk about a world where those walls are gone, or when they claim a country is moving that way. Though actually, speakers do not always mean it in a strict way. Sometimes they only mean “old titles and manners matter less now.” Sometimes they mean a hope that has never quite arrived. In British English, classless can also be a sharp everyday jab meaning rude or without good taste (“a classless remark”), but that is a different use, and not the sense we are filing here. The society sense is the one you will meet in history, politics, and the news.