This is a story about a man, Harry, dying on the slopes of Mt. Kilimanjaro as he and his wife await the plane they hope will take him to help. The man knows he is dying, despite his wife's reassurances.
At the point of this quote, death is coming for him. Before this, Harry used other metaphors for it—at first it is distant, likened to people on bicycles. Later, it is foreshadowed in the birds (vultures) hovering near. Now the dying Harry uses the metaphor of a hyena to describe death.
Hyenas are sometimes scavengers who eat the flesh of animals that have already been killed. In this metaphor, the animal is described as having bad breath and sitting on Harry heavily. This is a sensory image, as it conveys both smell and touch (weight), and it is an unpleasant image.
The quote is meaningful because it communicates to us as readers that Harry is near death. It conveys to us that he finds death unpleasant and that he is still fighting it, even to the end. The words of his wife, Helen, at the end, ordering the servants to move the cot, are also representative: as usual, the wife is unaware of the thoughts going through her husband's head.