The title borrows a military phrase, "surgical strike," for something clean, quick and supposedly precise. The poem itself is only four short lines, and it sets that language against everyday life. A war lasts half an hour, and it comes "from our want of discourse," meaning that it grows out of people failing to talk, or lacking the words or willingness to do so. The poem doesn't say who "we" are, so the reader can picture a quarrel between two people or a larger conflict seen from far away.
What stands out is how calm the speaker sounds. The violence is "ordinary as the afternoon," and then comes the line "home to supper." Fighting is over, and life carries on as if nothing happened. The mood is quietly unsettling. The speaker seems to feel a dull, uneasy resignation, and perhaps a hint of guilt, at how easily harm becomes routine. The flat tone makes the idea hit harder: if we can't talk, war can slip into the day like any other chore.