In Invictus, what is the meaning of "Looms but the Horror of the shade"?
One key to understanding "Invictus" is to know a bit about the author. William Henley contracted tuberculosis as a child, and had one foot amputated; doctors barely managed to save the other foot. Although he enjoyed short periods of good health, much of his life was spent in and out of hospitals, and his writing reflects this experience.
When Henley utters the famous line "My head is bloody, but unbowed" in the second stanza, he is referring to not giving in to despair despite enduring the pain and uncertainty of the disease that eventually killed him. The "place of wrath and tears" refers to the world of the living, in which he is both angry and sorrowful at what he endures as a man with tuberculosis. What lies beyond the pain and suffering of this life is "the Horror of the Shade", in other words, death, in which one becomes a shade or shadow of one's former self.
In this poem, Henley asserts that he will face both present pain and the horror of death with as much courage as possible.
In this line from Henley's poem, "the shade" is death. So the "horror of the shade" is the horror of death. And it is the horrors of death (as he puts it) that are all that looms after this life (this place of "wrath and tears."
So, in the context of the poem, this line is quite important. Henley has been saying (in the first two stanzas) that he can face (and has faced) everything life has to throw at him and he is wounded but still brave.
In the third stanza, he goes on to say that not even the horrors of death (in the line you cite) frighten him. No matter what, he is the master of his own fate.