A fateful blade indeed.
Spoilers Ahead
The Night King turned out to be fireproof, and even found a way to evade Jon Snow, but the demonic creature was eventually taken down by a tiny Valyrian Steel dagger, carried by Arya Stark.
That fateful dagger has had an enormous impact on this story, first making an appearance in season one, when Bran is bedridden, freshly crippled after Jaime Lannister pushed him out of a window.
A mysterious assassin attempts to murder Bran with the dagger, but is stopped by dedicated mother Catelyn Stark, who practically cuts her fingers to the bone trying to disarm the assassin. The struggle almost results in Bran’s death, but he is saved by his direwolf, Summer, who tears the assassin’s throat out. When the dagger is examined later, it is found to be made of Valyrian steel, with a dragonbone hilt, indicating a royal, possibly Targaryen, heritage.
This is Catelyn’s first clue that the assassination attempt came from someone of great wealth and importance, being too valuable a dagger to belong to the lowly assassin. Thus, Catelyn takes the blade to King’s Landing, where Littlefinger reveals that the dagger once belonged to him, before he lost it in a bet to Tyrion Lannister.
Of course, Littlefinger is telling blatant untruths, as usual, but the lie provokes Catelyn into arresting Tyrion, sparking tension between House Stark and House Lannister, eventually exploding into the War of Five Kings.
Ned Stark holds the dagger temporarily, but loses it to Littlefinger after he betrays him. Littlefinger quietly keeps the dagger until he arrives at Winterfell, several seasons later, and gifts the dagger to Bran Stark, who at this point, knows the history of everything, including the blade. Bran then gifts the dagger to Arya, in the exact same spot where she will later stab the Night King.
But Arya’s first use of the Valyrian Steel blade is to slice open Littlefinger’s throat, a most cathartic killing. It isn’t quite clear, but it seems likely that the dagger was Littlefinger’s all along, and that he was behind the assassination attempt, though this has never been confirmed; his motivation is a little murky.
Later, Arya uses the dagger to spar with Brienne of Tarth, and she uses the “dagger drop” move which will later prove so effective against the Night King.
Meanwhile, over at the Citadel, Samwell Tarly studies a book about the Long Night, the ancient victory over the White Walkers.
