Auden's poem "Unknown Citizen" consists mostly of an epitaph for a recently deceased person, followed by pointed questions in the last two lines. The poem has a unique perspective, that of various data-collecting bodies (government, employer, union, etc.) and their acknowledgement that the Citizen was an upstanding person.
What makes this poem satire is the juxtaposition of the last two lines in relation to the tone of the poem. The majority of the poem is a presentation of the fact that the Citizen did what was expected and never challenged any of the authorities over him. In the eyes of these data-collecting bodies, this is laudable. Yet, the last two lines ask if he was happy and free and assure the reader that there is no reason to ask about this kind of thing. Everything was all right.
The last two lines don't just come out of the blue; Auden foreshadows them with some of his statements. For example, it is clear that the Citizen only had opinions acceptable to the time in which he was living--"When there was peace, he was for peace: when there was war, he went." Also, Auden mentions Eugenics, which was a movement in favor of ensuring that "desirable" people reproduce and "undesirable" people didn't. Hitler took that movement to its extreme, but it was a significant movement in the United States, as well.
Unknown Citizen was written in 1939, at the end of the Great Depression and shortly before World War II. Kristallnacht had occurred the year before, so Hitler's danger was apparent, and yet there were strong voices in the United States that were antisemitic, refusing entry into the United States of refugee Jews from Germany. It was a time when a dissenting political opinion was important because the US government was holding off from intervening in events in Europe.
Ultimately, then, Unknown Citizen satirizes the concept, from a governmental and corporate perspective, of what a good citizen is--one who does not make waves.