"The Monkey's Paw" is narrated in the third person. The narrator is like a spider on the wall inside the Whites home, conveying and commenting on the events taking place there, but never joining in on any of the action. The narrator keeps description to a minimum, giving us just enough information to piece things together. He (we'll call the narrator a he) never tells us more than is absolutely necessary. For example, he could come right out and tell us whether the paw has magical powers. He could tell us exactly what happened to Herbert, and if it really was him knocking on his parents' door. Heck, he could even tell us what Mr. White's final wish was. But he doesn't. This narrator wants us to use our imaginations to answer these and other questions on our own.
The third-person narrator can even see inside the characters' heads and comment on their thoughts, making him omniscient (he knows everything). For example, this passage allows us to get inside Mrs. White's head:
Mrs. White [...] was very happy at the expense of her husband's credulity. All of which did not prevent her from scurrying to the door at the postman's knock, nor prevent her from referring somewhat shortly to retired sergeant-majors of bibulous [drunken] habits when she found that the post brought a tailor's bill. (2.6)
"Credulity" is a good word to know when reading this passage. It just means gullible. We bet someone's called you gullible before, like maybe an older sibling or friend because you refused to believe that the Tooth Fairy wasn't real…
In this passage the narrator is showing us not necessarily that Mr. White is credulous, but that his wife thinks he is. At the same time, the narrator is showing us that Mrs. White is probably just as susceptible to superstition as her husband. The day after Mr. White makes his first wish, the two hundred pounds is all she can think about all day long, especially when she gets bills in the mail instead of money.