The word 'class' fell out of favor during the Cold War. Over time, those in academia who continued to use it quietly altered its meaning; 'class' became just another element in the politics of identity. It was about the way you grew up; how you dressed and the way you spoke; what you did in the weekend. And with this drift into general stereotyping, the notion of class lost all of its explanatory power.A recent article in Jacobin magazine, excerpted from A People’s Guide to Capitalism: An Introduction to Marxist Economics", explains how Marxists use the term.
Hadas Thier argues that it isn’t about how much money you make, your cultural traits, or your level of education. Marxists hold that everybody who must sell their ability to work for a wage, and who can't produce the necessities of life for themselves, is a member of the working class. That's the vast and growing majority of society. Wealth and poverty do not determine class, rather, they are manifestations of it.
"You can’t understand either the worker’s or the boss’s class position without understanding that the whole of the system is one in which labor is set to work, in order to produce a profit for someone else. Class, in other words, is a relationship of exploitation."
If you've read Thier's article and want a more detailed introduction to the Marxist theory of class, check out this explanation from sociologist Khushdil Khan Kasi: