Many critics have opined that this poem contains a conscious or unconscious death wish. The very common interpretation is that the speaker, presumably Frost himself, finds the woods so "lovely, dark and deep" that he is tempted to walk into them and lie down in the snow to let himself freeze to death. This would suggest that he is a very unhappy man and even that he doesn't want to go home. According to this interpretation, the speaker is prevented from realizing his "death wish" because he is reminded of his responsibilities and obligations to other people, probably to a wife and possibly to his children. After all, what is he doing out on a snowy night in a horse-drawn sleigh if he didn't have errands to run. This is "the darkest evening of the year," that is, the longest evening, which would be December 21st, just before Christmas. He might have Christmas presents as well as food in that sleigh. He seems a little paranoid about being seen by the man who owns the woods. Furthermore, he must realize that he can't leave his little horse standing there. If the horse didn't freeze to death itself, it might decide to go on to the nearest farmhouse, and then a search party would be out looking for the speaker. Or another traveler might come along and see the horse and sleigh and stop to investigate. There are strong arguments to favor this "death wish" interpretation. But Frost himself repeatedly denied that he had any such idea in his mind. Some writers, including his biographer Jeffrey Meyers, have actually argued that Frost did not understand the meaning of his own poem.

It is strange that the speaker would stop on one of the darkest evenings of the year. Even the "little horse" thinks it is strange. No doubt, the speaker had seen snow many times. Why did the speaker stop with miles to go before he sleeps? The promises keep the speaker from staying in the "lovely, dark and deep" woods. As mentioned above, the promises could be responsibilities with which the speaker feels an obligation. It is no time to give in to weariness of life.  

You have to look at the line in context:

The woods are lovely, dark and deep

But I have promises to keep

And miles to go before I sleep

And miles to go before I sleep

It isn't just that he has to fulfill certain promises that he has made to others before he dies, he also has plenty of life left to live. The miles are time. It also seems to imply a certain power over death. The speaker is not willing to die until he has kept his promises and served his time.

Here's a link to an article in the Writer's Almanac that provides the original story behind this poem by Frost. Read it, and you see that his experience suggests that the lines refer to a sense of obligation he felt.  http://writersalmanac.publicradio.org/index.php?date=2012/03/07

This poem always gives me the creeps, but it is very moving.  The way I see it is that the speaker has stopped to reflect on life.  Sometimes life gets overwhelming, and it is tempting to just give in.  The speaker decides not to give in to death.  The promises are ones he made to himself and to his loved ones to keep going, keep fighting, and keep living his life.

The speaker in the poem is sometimes considered to be thinking about approaching death while musing about the lovely but dark and deep woods. If this is the case, the speaker isn't ready to die yet. There are responsibilities that must be addressed before laying down to "sleep".

Lots of ways to interpret this one.  The most "literal" meaning would simply be that the speaker does not have the time to just hang out in the woods and enjoy nature.  He has things that he has to do, things that he has promised to get done.