The dark and stormy night and the isolation of the house add to the eerie nature of the setting and reinforce the spooky nature of the plot.
Setting helps create a mood by making things seem possible. In a dark night, it is easier to create a dark mood. It is raining, and the road is boggy. The house is isolated because it is far out in the country and there are a lot of empty houses on the street.
"That's the worst of living so far out…of all the beastly, slushy, out-of-the-way places to live in, this is the worst. Pathway's a bog, and the road's a torrent. I don't know what people are thinking about. I suppose because only two houses in the road are let…
Even without explicitly saying something bad is about to happen, the rain and lonely house foreshadow trouble. The reader will not be surprised when a magic monkey paw appears, and danger follows. After all, how can something good happen on such a dark night?
It is also important to note the contrast between the family before the sailor arrives and after. Yes, it is raining outside. However, there is a fire going and things are peaceful inside. There is a mostly homey scene. When the sailor arrives with the paw, there is mention of how isolated the house is and how bad the road is. This is no coincidence. The reader is being told that things are good, but they are about to get worse.