Often, but not necessarily, determined by income, and certainly not due to some inbred genetic superiority or inferiority. I see a class as a category of people with similar economic or social interests that tend to react together as a group. It's sort of like the concept of "region" in geography, you draw the boundaries subjectively, but you essentially have an area where those boundaries imply some sort of homogeneity.

The Marxists see classes as produced by technological innovations in the means of production and the organization of capital. They have identified many, but the ones you here most about are the bourgeoisie,
and the proletariat, which roughly correspond to the ownership/commercial class and the industrial workforce, respectively. Marxists believe different classes have different interests and tend to organize together to protect their interests against other classes. They believe because of this, classes are often in conflict with one another, and this force drives history.

Classes can be defined strictly conveniently for narrow purposes of description (Bohemian: the intellectual poor, people of higher than average education who consider themselves as members of an urban, artistic, avant-garde community). Or you can define a group because you suspect they will have a tendency to vote uniformly and predictably on certain issues: The Managerial/Professional class, (not to be confused with the entrepreneurial/ownership class). You can also define them with purely economic criteria ( the aristocracy of labor - Highly Skilled Workers, people like skilled machinists or computer programmers who are highly paid because they possess a valuable skill).

This does not necessarily imply there is no class mobility across generations, or even in one person over time. The child of a skilled worker may be a Bohemian student working on a professional degree.

And of course, we define classes economically too, by strict dollar limits,
from low to high, or by their place in a hierarchy. One classification I'm working on:

Those who don't work
Those who work for others
Those who work for themselves
Those who have others work for them
Those who don't have to work at all

So just what do we mean by "Middle Class"? We do use this term all the time.