What significance does the word "But" have in the last verse (i.e., "The woods are lovely, dark and deep /. . . And miles to go before I sleep") of the poem "Stopping by Woods on a Snowy Evening" by Robert Frost?

The word "but" in the final stanza reveals the fateful choice of direction that the speaker has made.
He'd flirted briefly with resigning himself to an easeful death: to penetrate deeper into the "lovely, dark" woods, as he calls them. But—and there's that word again—he has much in life he still needs to do; that is to say, he has "promises to keep." No matter how "lovely, dark and deep" the woods may be, the speaker won't succumb to their temptations: he will go on.
Another valid reason for avoiding the woods is that the speaker has miles to go before he sleeps, (i.e., a lot of life still left in him before he finally gives in to death). The fact that this line is repeated right at the end of the poem indicates the importance of the direction that the speaker has chosen to take.
https://www.poetryfoundation.org/poems/42891/stopping-by-woods-on-a-snowy-evening