The narrator stops because he wants to **enjoy the scenery of the forest**. Assuming that the journey the narrator has to make is an extensive one ( _miles to go before I sleep_ ), the narrator wants to take a small break to watch the natural wonder of the snowfall and the beauty of the trees.
There are several lines that support this idea:
> To watch his woods fill up with snow.
This is the clearest statement of the purpose of the narrator stopping in the woods.
> The only other sound’s the sweep
>
> Of easy wind and downy flake.
This could be interpreted several ways, but to me, I see this as the narrator's wondrous appreciation of the heavy snowfall.
> The woods are lovely, dark and deep,
This line hints that the narrator wants to spend more time observing the forest, but he has commitments to main and thus, has to continue on his journey.