The film begins with K seeking out Sapper Morton, an older replicant model to kill him. It ends with K dying on the steps after leading Deckard to his daughter who was a miracle baby born between two replicants, Deckard and Rachael. Between these two points we watch K go on a journey of what it means to be human. K receives a personal connection with Rachael as he has been implanted with a memory of her that he believes is his own. The reality is that the memory belongs to Dr. Stelline who designed his memories, and who is Rachael and Deckard's daughter hiding in plain sight.
K is hunting down and destroying his own kind, replicants. He is simply doing what he is programmed to do. But with this comes a deep connection to search for the truth. And the reality of this comes to life because that truth he seeks is directly related to the life he believes he lived (as Rachael's son). And as he uncovers the truth that he is not Rachael's son he still feels deeply within him the desire to do what is right on the side of life. Rather than taking life, he seeks to unite it. K becomes the connection between what was and what is, represented by Deckard and his daughter Dr. Stelline meeting for the first time. And in doing this he finds a bit of peace in his life, even as it tragically ends saving Deckard.