In W.H. Auden's "Funeral Blues," the speaker is preparing for the last line of the first stanza, which introduces the theme of death, as found with the words "coffin" and "mourners."
All poetry speaks to different people in a variety of ways. For me, in light of the death the Auden is writing about, it seems that he is commanding that things which occur normally in an everyday world should be stopped. For while the world never really stops for anyone or anything, the speaker notes that here, things should be different.
Stop all the clocks, cut off the telephone...
Clocks that measure time should stop: for those affected by this death may well feel that time has stopped in light of their loss. Telephones should be "cut off" or disconnected, so that communication stops: no one may call in or out. Today is much different than yesterday was.
Prevent the dog from barking with a juicy bone...
Even the dog, in a state of oblivious delight with his "juicy bone" should be silenced, though he would not understand why: for it would appear that the principle of the situation governs the speaker's thoughts.
Silence the pianos and with muffled drum ...
The piano may be associated with gentleness and love—or even with light-hearted entertainment. In this case, however, they must be quiet. The drum is muffled for a British military funeral (and Auden was born in York, England)...
Muffled drums accompany the graveside processional.
...but the "muffled drum" should be further silenced so it makes no sound.
When all of this is done, perhaps we can (as readers) imagine that life, in general, must stop because someone dear, someone truly fine has died. I sense that this is a person of greatness, and I am reminded of Hamlet's line to Horatio regarding his own father's death in Shakespeare's play by the same name:
I shall not look upon his like again. (I.ii.194)
For me, this line means that never will someone so marvelous walk the earth again.
The speaker notes that the mourners, in this appropriate—quietly respectful—setting, may now come to pay their respects to the person being laid to rest.
Bring out the coffin, let the mourners come.
This is my impression in reading the first stanza. But, one should note that the poem was not written with serious intent:
The 1936 five-stanza version was a satiric poem of mourning for a political leader...
Written at one time for a play, it now stands alone as a piece of Auden's verse. And out of its historical context, it seems serious enough. The only evidence that it is satirical (at least in the first stanza) may be the mention of the dog—for who would seriously ask that a dog's actions be limited or altered because of the death of a human being?