Frost counter balances two different worlds in this poem: the world of civilization with all its responsibilities and natural world offering solace and relief.
The speaker of the poem is drawn one evening to leave the village and go out into the silent woods. It is dark and snowing...these may symbolize death. The speaker, like the reader, may be world weary and need escape from the demands of his life. It is important to note the title of the poem, the escape he seeks isn't permanent.."he is only stopping by"not intent on ending his life ...the relief he needs is offered by the silence of the natural world.
We can all identify with what the speaker is feeling when the world has been too much with us and we just need some kind of solace. His little civilized horse doesn't understand though and shakes his "harness" (cause he is harnessed by civilization) bells to remind the speaker that what ever he is doing alone in the woods in the dark in a snow storm isn't normal ("queer"). And the speaker returns to the village and the civilized world of promises and obligations. There is a definite though subtle attraction to leaving all of those demands behind but nevertheless the speaker values his commitments and obligations enough to return to them.
One interpretation of "Stopping by Woods on a Snowy Evening" that must be inferred rather than seen from context is that the narrator is not on a business trip at all, but rather on a journey of personal discovery. His line of purpose, "promises to keep," is maddeningly vague, and could mean any number of things. If one interprets his longing for the woods as a desire to return to his simpler life, then he could be traveling to "find himself" and feeling a pang of regret.
Another possibility is that the narrator is leaving his hometown permanently. He speaks of knowing the owner of the woods, and his horse being accustomed to stopping at farmhouses. If he is leaving for the last time, the woods might be a part of his past that he is leaving behind, an unworried and careless symbol of youth that he must now shed to become a responsible adult, one who must "keep promises."
Finally, one very common interpretation is that the narrator is contemplating suicide. In this interpretation, the narrator is looking at the woods for solace from his troubles; he could walk into the snow and succumb to hypothermia, going to his final "sleep" without seeing to his obligations. However, he turns away from the woods and continues on, feeling that he must fulfil his promises ("miles to go") before he can think selfishly of himself.