The Night king wants to kill Bran because Bran is the only one who has the ability to cut him. Not as in kill him or cause actual harm however with his capacity to see the past, he can warg himself back to the time he was made and discover pieces of information on how he and his military can be vanquished.
Obviously Bran is the three peered toward raven now so he knows all that ever was or will be. That makes him pretty important.
Night King wants to erase the world and Bran is its memory. As the Three-Eyed Raven, Bran has the capacity of greensight, which implies he can see occasions previously, present, and future through dreams. Executing Bran would basically delete all memory of humankind. Samwell Tarly clarifies it quite well in the scene.
There are numerous hypotheses drifting around with respect to Bran and the Night King however we definitely should be pondering “For what reason does the NK need Jon Snow”? He is by all accounts after Jon solely, simply check how circumstantial both their appearances are.
Jon is a kid conceived of ice and fire. Jonin the books at any rate has repeating longs for all the rulers of winter in the graves at Winterfall rising once more.