The speaker stops in the middle of the woods to admire the beauty of the scene. However, as much as he admires the beauty of nature, he also has a sense of darkness and/or the forbidden. The words "frozen" and "darkness" suggest the notion of death. The speaker considers going further into the woods to experience both the beauty and the darkness. This is an interesting moment wherein he appreciates the beauty of nature but also, in considering his own mortality, he considers the allure of death as sleep which may be as calm and beautiful as the scene he looks upon. Thus, death would be an escape from life's responsibilities ("promises"). The woods ("lovely, dark and deep") could also suggest something forbidden, a sexual liaison perhaps, or some taboo desire. Ultimately, he chooses life and responsibility ("promises to keep"):
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.
The repetition of the last line indicates significance. He literally has miles to go before reaching his destination and, figuratively, miles to go until the end of his life. He considers pursuing the dark and lovely woods. Interpretations vary, the poem is vague; this could mean he considers his own death or he considers something more seductive or even sinful, dark and beautiful. The "But" indicates that, after considering the "lovely, dark and deep" allure, he chooses his life and responsibilities ("promises").
In the simplest analysis, the speaker notes that whoever owns these woods, the property owner, is not present and therefore won't mind if he stops to have a look. But the poem is open to multiple interpretations. One could interpret the owner of the woods as God, especially since the speaker is concerned about being seen (and/or judged) as he considers either his own mortality or some other dark and lovely desire. In this interpretation, the speaker feels God's gaze/presence/instruction, and therefore chooses life, responsibility, and to keep his promises.