In many ways, the term “social class” is something of a misnomer when we are talking about Karl Marx’s ideas. Class really has nothing to do with society and with social interactions. Instead, class is, for Marx, all about what he calls the “relations of production.”
In any economy, there are factors that are called the “means of production.” Economists call these “factors of production” or “resources.” They include land, labor, and capital. Marx says that the classes in a society are determined by who owns the means of production. This is what “relations of production” means. The relations of production are the relationships between those who own the means of production (other than labor) and those who only supply the labor.
It is this relationship to the means of production that determines what class you are part of. It is not whether you have gone to college, or what race you are. Instead all that matters to Marx is whether you own the means of production.
Thus, class, to Marx, is determined by whether a person owns the means of production.