Summary:Aliens arrive and the military (via Colonel Weber) hire Louise Banks to do the translating. She succeeds.... perhaps too well.
Meanwhile, interspersed with the alien narrative is Banks addressing her child in the future tense discussing memories. The point of these sections is a spoiler.
Commentary with Spoilers:When I first read Chiang, I read him wrong. I kept expecting something that he wasn't doing. Chiang is old-school SF. He squeezes all he can out of an idea.
Here the idea is language: What if you could read a language, not sequentially, but wholly at once? The shape of the aliens--not bilateral like us, which caused us to read sequentially, Chiang's story hypothesizes--is radial symmetry (that is, the same all the way around). So their language absorbs all information from the past, present and future. This in turn shapes their thinking so that they actually perceive future and past simultaneously.
When Banks grasps this, her brain alters so that she can perceive the future and the future child it contains--a child who will die. This is emotionally poignant--one of Chiang's more powerful works.
Chiang's idea rests, in part, on the Sapir-Whorf hypothesis that states language shapes the mind. This notion was discredited, but has reemerged with new nuances. Here are one and two articles from Scientific American that suggest that words can at least sharpen our awareness to what can be observed. This is SF, after all. It's aim is to get you think, not necessarily describe the universe perfectly. Who knows? Maybe a language will get us to grasp the universe in completely different terms.
When Colonel Weber arrives, the narrative is uncannily familiar. It took a minute to recall that it rang of the opening to Samuel Delany's Babel-17. No doubt this is an homage to Delany's own investigation into Sapir-Whorf.
The original idea that inspired Chiang's story is Fermat's principle of least time. Normally, in physics, we say that light travels in a direction at the speed of light until it hits a new medium where it slows a changes direction. Fermat suggested that light (as if it had agency of its own) arrives at its destination because it is the fastest route to get there, not a straight line, because it can travel faster in the first medium than the second. The way this applies to your own life might be traveling on the interstate as far as you can before entering city streets. You might overshoot your destination if you didn't have drive as long on the slower city streets. To see how this applies to the story in question, see quote below.
"[T]he ray of light has to know where it will ultimately end up before it can choose the direction to begin moving in."