"The darkest evening of the year" would be the night before the Winter Solstice (December 21), which is the longest night of the calendar year. The man in the poem is riding his horse through the woods on a snowy December evening, and he stops to contemplate the beauty of the woods as they "fill up with snow". As much as he would like to remain in the quiet splendor of the snowy forest, the man realizes that he has responsibilities and "promises to keep". He has "miles to go" before he arrives home, so he is forced to drag himself away from the peaceful scene and head home.
In response to the answer posted above, a different construction could be put upon the phrase 'miles to go before I sleep'. Instead of referring literally to the speaker's journey home, it could also be symbolic of death.
To look more closely at the final stanza, where this phrase occurs, we can see that this particular line is repeated, which gives it a certain emphasis. The first line of the stanza paints a picture of the woods as being tempting, seductive, as though luring the speaker to remain: 'The woods are lovely, dark and deep'. It is as though the speaker wants to surrender to the sheer deep peace and quiet which surrounds him - in effect to yield to a kind of death, an everlasting stillness.
But then, in the next line, as though with a mental sigh the speaker rouses himself as he recollects the duties of life: 'But I have promises to keep'. He still has responsibilities to discharge, the whole business of life to get through, the 'many miles' of life's journey to travel before he can give in to the profound stillness of death and eternal rest, a sweet sleep in which he can bury all the cares of life.