Plain and simple, this poem made me feel sad. My mind immediately jumped to those Sherlock Holmes episodes, or other old murder mysteries, where the dark figure ghosts through the damp, gloomy alleyways and streets. Except this time the figure was just a sad and lonely soul.
The first two stanzas are basically Frost saying that he has been there and back throught "the night," which I took to mean a state of depression and loneliness. He has experienced more bad turns in life than most. He also says that he has passed "the watchman...[dropping his] eyes, unwilling to explain." To me, this sounded like when someone who has recently experienced a tragedy shies away from curious bystanders, not wanting their sympathy or questions. Frost is stuck in "the night," and is either too ashamed or too upset to talk with anyone about it.
The last three stanzas, Frost talks about the sounds that have echoed to him through the night. First, the sound of "an interrupted cry," which does not "call [him] back or say good-by." This cry does not come from a person who particularly cares about him, it neither wants him to stay nor is going to miss him if he leaves. The hopelessness of knowing that no one is concerned about him only adds to the resigned and despondent tone. The last thing Frost notices in his journey through the night is the sound of "one luminary clock against the sky [proclaiming] the time was neither wrong nor and right." From what I have found, the clock he was referring to was Big Ben, which has been the site of many suicides. Basically, this apparently impartial and seasoned mediator seems to be telling Frost that his presence in "the night" was not necessarily a right or wrong thing, it was just the way his situation had turned out. And that is how Frost's entire poem spoke to me: it was not that his being "acquainted with the night" was not the right or wrong thing, he was just telling people his story in the best way he knew how, which happened to be a very concise and grave poem.