The underclass means the group of people at the very bottom of a society — very poor, often without steady work, and, this is the important part, stuck there, with little realistic way out for them or their children. That last idea is what separates 'underclass' from simply 'the poor': it carries the sense of being shut out of normal society for a long time, maybe across generations. It is a word from sociology, politics and journalism, not everyday chat; you will meet it in newspapers, textbooks and speeches. It is also a word people argue about, and your students should know that. Some writers use it with sympathy, to point at a system that traps people. Others use it to blame the people themselves, as if they were a different sort of person from the rest of us. Because of that second use, many sociologists now avoid the term, and calling a real person 'underclass' can sound cold or insulting. Say 'people living in poverty' when you are talking about individuals, and keep 'underclass' for describing the structure of a society. Grammatically it is almost always singular and takes 'the': 'the urban underclass', 'a growing underclass'.