Wilfred Owen tells of "horror" in his poem "Dulce Et Decorum Est." Explain what he means by this "horror."

Although the word "horror" is absent from the poem, Wilfred Owen describes the horror of war through a series of images.
In the first stanza, a group of fellow soldiers are returning from battle. They are emotionally and physically exhausted. Many of these soldiers have lost their boots, and as a result, their feet are bleeding. This is already a depressing scenario, but there is more to come in Stanza Two.
Stanza Two is when the "horror" begins. As the soldiers are making their way home, gas shells explode all around them. The men frantically pull on their gas masks, but one man is seen "yelling out and stumbling." Owen doesn't tell us whether the soldier is missing his mask or is simply too slow in pulling his mask on. In this stanza, the poet talks about the soldier "drowning" under a "green sea." The green color very likely refers to chlorine gas, which was used during World War One (the setting of the poem).
The third stanza describes the soldier's excruciating death from gas poisoning:

In all my dreams before my helpless sight,
He plunges at me, guttering, choking, drowning. 

The "horror" comes from both the manner of the soldier's death as well as its reoccurring image in the form of flashbacks in the poet's mind. The poet is forever haunted by this disturbing imagery. He will never be free from the terror of such a moment as long as he lives. Essentially, the "horror" is replayed in his mind over and over again.


...watch the white eyes writhing in his face, 
His hanging face, like a devil’s sick of sin; 
If you could hear, at every jolt, the blood 
Come gargling from the froth-corrupted lungs, 
Obscene as cancer, bitter as the cud 
Of vile, incurable sores on innocent tongues--

During World War One, soldiers who were exposed to chlorine gas died very painful deaths. The poison gas caused burning eyes, vomiting, intense stomach pain, severe headaches, and "incurable sores" on tongues. In other words, the last stanza perfectly describes the "horror" of such a death. Eventual demise comes from what is called asphyxiation or suffocation.
 
The poet portrays war as a thing of horror. He explains that too many people quote the phrase Dulce et decorum est Pro patria mori (It is sweet and fitting to die for one’s country) without truly understanding the consequences of war. Through a series of disturbing images, the poet reinforces the human suffering that has been caused by war.
 

 
http://www.vlib.us/medical/gaswar/chlorine.htm