The speaker of "A Wish" lists out his dying wishes. Basically, he is unconcerned with what people usually worry about when they expire.
He insists that anyone may visit his deathbed (even if they are only hoping for an inheritance), and that anyone can weep for him. Further, he does not want a funeral in a crowded room, where friends gape at his body and then leave. He also does not want a famous doctor to visit his deathbed, only to fail at providing a diagnosis.
What the speaker does wants from death is the freedom that his life does not provide. While he is dying, he would like to be placed before a window so he can look out over the landscape. The sight would help his soul mirror its beauty, leaving him "composed, refreshed, ennobled, clear," instead of focused on his sick room.
Since Arnold's work often criticizes the modern way of life, it seems fitting that his poem about dying would also criticize modern attitudes on death. In effect, what the speaker of "A Wish" wants is that his dying days be focused on the good of his soul, and not on the external trappings of the physical, superficial world.
At the beginning, he hopes that people will be allowed to have their individual reactions, rather than being expected to act a certain way. This wish aligns with Arnold's common desire that people work to realize their own desires, rather than conform to the demands of modern society. If others need to cry at his death, they should. What he does not want is the pomp, circumstance, and pretentious solemnity of a typical funeral. The implication is that such rituals are only about external pretense, and not about the true feelings of the soul and the individual.
As he often does, Arnold relates the soul's power to the natural world and its beauty. He hopes that his final days will be not about the expiring of his physical flesh, but instead about the potential of his inner soul. He wants to spend those final moments transfixed on nature, reflecting on "the world which was ere I was born/the world which lasts when I am dead." The natural world is the only part of the world that continues on in spite of human changes and modernization, the only part of the universe worth celebrating in his final days. Thus, this is what he wants to see when he dies. It will both improve his spirit and comfort him to remember that life will go on even if his own little life has ended.
The poem's elegiac tone is reflected in its structure. It has a set meter, iambic tetrameter, and a set rhyme scheme, ABAB. It does not deviate, and there are no surprises. This represents the speaker's steadiness and acceptance of his death; he is not afraid, and he speaks his wishes and desires calmly. His emotions are not erratic, since he is not worried about death. Instead, he knows what matters most to him, and finds serenity and comfort in that.