When the speaker says, “The woods are lovely, dark and deep,” he is talking about the forest in front of him. The woods look beautiful because the snow is falling gently. They are also dark and deep because it is evening, and no one is around. This quiet, peaceful, lonely forest feels very attractive to the speaker. It feels like a place where he can rest. 

However, the wood is also “dark and deep.” It feels like a place where someone can die. The speaker’s wish to stay there longer hints at a deeper feeling. Maybe he is too tired and sad. He wants to escape from life completely.

But the speaker suddenly remembers that he cannot stay there. He says, “But I have promises to keep.” This means he has duties and responsibilities to fulfill. People depend on him. Hence, he says, “And miles to go before I sleep.” Here, “miles” represents the rest of his life. “Sleep” means final rest or death. So, he is saying that he still has many duties to complete before he can take his final rest.

In these lines, Frost shows the conflict between rest and responsibility. The woods attract him, but life reminds him to move forward.