In just three lines, the speaker tells us they were present at an execution at noon, and then that rain fell on their hat the whole way home. The poem never says what the speaker thinks or feels. It gives us the event and the walk afterward, and leaves the rest to us.
That restraint is the point. The flat, matter-of-fact statement of the execution, with no explanation or reaction, suggests shock, or a numbness that has no words yet. The title, "Witness," hints that the speaker is watching rather than acting, and perhaps carrying some weight from that. The rain does the emotional work instead. It stays with the speaker "all the way home," as if the experience can't be shaken off, and the sound of it on a hat is quiet and steady, like a mind replaying something. The mood is somber, hushed, and heavy, and the short lines make the silence feel real.