(To JS/07 M 378 This Marble Monument ?Is Erected by the State)
The epigraph lets us in on a secret: we’re reading a dramatic poem. It’s all an act. The poem is pretending to be an official celebration of a dead person: the Unknown Citizen. The words are inscribed on a "marble monument" that was paid for by the State, or government.
Which government? We don’t know. But referring to "the State" makes it sound very ominous, like George Orwell’s "Big Brother" from 1984.
Marble isn't cheap, and most people can’t afford to use it as a building material.
The government, however, has seemingly infinite financial resources to work with, because it takes money from everyone.
As for "JS/07 M 378," we think Auden is just having fun by stringing a bunch of letters and numbers together in some incomprehensible way.
It seems that "JS/07 M 378" is how the Unknown Citizen is identified, and the monument is dedicated "To" him. Referring to people in this way is, obviously, very cold and impersonal, but it can also be convenient, so bureaucrats do it all the time.
To give a chilling but relevant bit of context, at the time this poem was written, the Nazis were already starting to identify Jewish prisoners with numbered tattoos, though this is not something that Auden would have known. But, in retrospect, this grisly parallel makes the "marble monument" seem that much more sinister.
By the way, the monument is clearly a parody of the Tomb(s) of the Unknown Soldier, found in many different nations and dedicated to soldiers who died anonymously in battle.
One of the most famous of such tombs lies underneath the Arc de Triomphe in Paris, which is a marble monument. You can read more about the Unknown Soldier in "What’s Up With the Title?"