Understanding Eliot's point requires a familiarity with the history of thought, modernity, the works of philosophers like Nietzsche, and a whole lot else that can't be easily summarized in a bite-sized internet article. Nonetheless, I will try to explain it in a few paragraphs:

First Things: Eliot drew a fruitful distinction between the upper class and the elite. Class is inherited from one’s ancestors and is thus tied to family and to a place. Membership in the elite, in contrast, is acquired through the mastery of certain subjects and techniques, typically in selective cosmopolitan universities.

His first point is that there is a difference between "cultural class" and "elite ability." This is not obvious to those of us in the Americanized western world, which is very technocratic. That is, in the American conception of upper class, wealth is a pre-requisite. We typically can't imagine someone being upper-class and poor or not-rich at the same time - which was a reality for a huge portion of the upper class for the vast majority of history.

FT: As Eliot argues, class is inherently conservative and provides a rich soil for literary and artistic creativity, while a society dominated by elites loses the continuity of inherited tradition and suffers from a sterile obsession with artistic novelty.

We can see this phenomenon playing itself out in contemporary art. The art world at the moment is essentially without an "inherited tradition" and consequently you'll see a lot of work which is shocking or novel for (arguably) no reason other than to be shocking and novel. See Tracey Emin, Damien Hirst, etc. for some examples.

FT: Corresponding to Eliot’s distinction of class and elite is a distinction between “levelers” and populists. Levelers seek to destroy the stratification of class, and with it the integral life of the nuclear family and local community. Populism, in contrast, can be a reasonable and wholesome reaction to the dominance of elites. It is often a natural ally of conservatism.

Eliot's idea here is that "levelers" are trying to level-out differences and remove hierarchy. Whether the levelers are poor socialists, rich technocrats, or somewhere in between, they are seeking to remove the existence of different value systems and hierarchies in favor of a single one. In the capitalist west, this is typically a sort of bourgeois-middle-class sort of value system, but of course that's an over-generalization.

FT: Unlike Marx, Eliot does not define class in terms of economic or political function. For him, classes are defined in terms of a shared way of life, acquired primarily through family and secondarily through education, clubs, forms of recreation, and other small-scale, face-to-face association. Entry into and out of class requires at least one generation, often several.

Now, this is a problem for Eliot, because he sees the upper classes as culturally separate from the lower classes. That is, the difference between the lower class and the upper class is not money or wealth - it's an entire culture, one in which he is interested in preserving.

He then goes on to explain why he thinks a culture created largely by lower-class values leads to a focus on commercialism, novelty and distraction. Populism, according to the author, is a sort of bulwark against this, as it prevents the technocratic elite from supplanting the historical upper-class culture. I don't think the thesis of "Eliot was a populist" is very fleshed out in this essay, though.