大気圏 means “the atmosphere,” the layer of air surrounding Earth. In the song, the image of passing through it at 350°C while the wings melt gives the myth of Icarus a vivid, space-age twist, making this a memorable and evocative word.
IKAROS takes the old Greek myth of Icarus, the boy who flew too close to the sun on wax wings, and turns it into a love song that burns up on purpose. The singer gets "君の瞳に近付き過ぎたの" (I got too close to your eyes), and the eyes become the sun. Then comes the strangest, best line in the song: "大気圏通過350℃" (passing through the atmosphere, 350°C). It reads like a reentry readout, and right after it "翼が溶けてゆく" (my wings are melting) and "どこまでも墜ちてゆく" (I keep falling, endlessly).
What makes it sting is that the singer does not want rescue. The chorus asks "笑ってよ" (laugh for me) and "燃やし切ってよ" (burn me all the way) until nothing is left to regret, hoping "燃え尽きますように" (that I burn out completely) so not even a speck of memory remains. In the middle, the English "Falling, falling down" repeats like the drop itself, and the singer drowns the fall in "異國の酒" (foreign liquor). A learner tip: 異國 is the old-style spelling of 異国 (foreign country), and the ending 〜ように turns a line into a wish, as in "振り返らぬように" (so that I never look back).