In book 22 of Homer's Iliad, Achilles and Hector meet in one final conflict. Hector is the last living Trojan outside the city walls, and he goes to confront the furious Achilles, thinking that it would be better for them to clash at once than put off their meeting any longer.
Then Achilles draws nears, and here we have the quotation in question: “Achilles approached, brandishing his great spear, and the flashing of his arms was like fire or the sun when it rises.” The simile is an especially vivid and meaningful one. On a literal level, the light is probably reflecting off of Achilles's spear and armor, making it glow brightly, almost blindingly, as he comes up to Hector.
However, we can see a deeper meaning here as well. Achilles is in a towering rage, and his anger makes him extremely strong. It appears to radiate off him, almost like he is glowing from the inside out with a fire that could consume Hector, and perhaps the rest of Troy, in an instant. The similes of light and the sun point to that radiant rage.
Further, we must remember that Achilles is not fully human. His mother is the sea nymph Thetis, a minor goddess. Achilles' super-human nature may well be shining out through his fury, and the brightness of his armor symbolizes that.
In any case, Achilles is as bright as a flame or the rising sun as he approaches Hector, so it is no surprise that Hector runs off in the opposite direction.