A class is a group of people who all think of themselves as being in the same kind of position in a country. The Victorians were very keen on classes because it gave everyone a reason for doing better: they were able to move from one class up to the next. As a result, each kind of job was related to a class. It also affected how you were called. Upper middle class used to call each other by their surname (Homes, Watson), while upper lower class were entitled to be called Mr, Miss or Mrs by the other staff in their shop or among staff in a house.
We still have a kind of class system now, but now it is based on education and shared interests rather than wealth and family.