The allusion to Icarus is made after W. H. Auden observed in Brussel's art museum a painting by the Flemish artist Pieter Bruegel entitled, The Fall of Icarus, the mythological son of Daedalus, who constructed wings of feather held by wax which enabled them to fly.  When Icarus donned these wings, he became so ecstatic in his ability to fly that he ignored the warnings of his father not to get too close to the sun because the wax would melt and the wings would come apart.

Auden's poem was written after his visit to the museum in 1938 in which he noticed how the painter minimalized the significance of Icarus's plummeting into the sea in his pastoral scene.  In his mind, Auden likened this marginal notice of man's misfortune to the defeat of the Loyalists in the Civil War of Spain, a defeat which received peripheral notice in the rest of Europe despite the fact that this war gave rise to Fascism.  Auden's poem "Musee des Beaux Arts" reflects this idea as he depicts the horror of universal apathy:

...That even the dreadful martyrdom must run its course

Anyhow in a corner, some untidy spot

Where the dogs go on with their doggy life and the torturer's horse

Scratches its innocent behind on a tree....

...and the expensive delicate ship that must have seen

Something amazing, a boy falling out of the sky,

Had somewhere to get to and sailed calmly on.

In Greek mythology, Icarus is the son of master craftsman Daedalus, who creates wings for each of them in order to escape from Crete.  The wings were held together by wax, and Daedalus warned his son not to fly too close to the sun--for obvious reasons.  Probably for equally obvious reasons, Icarus did just what his father warned him NOT to do, and he fell to his death. 

The poem begins with the comment that "the Old Masters" (the great artists whose works are apparently hanging in this museum) "were never wrong" about suffering--if it doesn't happen to you, it doesn't matter very much. The poem's narrator uses Brueghel's painting depicting the fall of Icarus to prove that point. 

"...the ploughman may
Have heard the splash, the forsaken cry,
But for him it was not an important failure...."

The farmer was not affected by the incident, so it didn't matter to him.

"...and the expensive delicate ship that must have seen
Something amazing, a boy falling out of the sky,
had somewhere to get to and sailed calmly on."

Again, personal tragedy is just that--personal.