This is a fascinating question, because at first glance it is hard to work out what the meaning is in this excellent tale of suspense. However, for me, the meaning of the story comes at the end of the tale, when the internal conflict of the barber is resolved as he decides not to kill Captain Torres and he seems to recognise both his place in the world, and also the place of Captain Torres:
But I don't want to be a murderer. You came to me for a shave. And I perform my work honourably... I don't want blood on my hands. Just lather, than's all. You are an executioner and I am only a barber. Each person has his own place in the scheme of things.
It is this recognition of every person having their own place "in the scheme of things" that suggests that the barber comes to have a grudging respect for Captain Torres, because he recognises that every person has a specific role in life that they are made for, and that they are made to do to the best of their ability.
What is key to this theme is the final paragraph, where we, along with the barber, are shocked to discover that Captain Torres new all along that the barber was a rebel:
In the doorway he paused for a moment and said, "They told me that you'd kill me. I came to find out. But killing isn't easy. You can take my word for it." And he turned and walked out.
What is interesting is that this final paragraph suggests that Captain Torres has also gained grudging respect for the barber. We know that Captain Torres is an executioner, and thus it is surprising that he lets the barber live and walks out. Perhaps he too has come to have a grudging admiration for the barber and his recognition of his place in "the scheme of things." It also suggests another side to the supposedly brutal Captain Torres, a side that shows it is not easy to kill, maim and torture.