The warmth in Natasha Romanoff/Natalia Romanova's voice as she recounted her version of the tale of the Winter Soldier and his Black Widow persuaded James Buchanan Barnes to remain with her in S.H.I.E.L.D. He knows of three different sets of memories, each of them incomplete. The first set belongs to Bucky Barnes: there are always women in those memories, but there is also a brother and a childhood best friend named Steve Rogers. The second set belongs to the Winter Soldier: there is blood and killing, but there is also a beam of light, a princess who bears a resemblance to Natalia. When James retrieves these memories from the files in his mind, it is like watching television. He knows how the plot has developed so far, but that's just it: he's not an active character in that storyline.
But now the third set of memories is an empty jar for him to fill. This is his and his alone to keep because he is actually participating in and directing the story. So he fills it first with his new memories of Steve and Natalia, accepting the two as a significant part of the past he can't remember and his closest friends. He doesn't know what will happen next, but all he knows is that he is free of the chains that bound him to Russia.
When Natalia concluded her tale, she admitted apologetically that a Director Fury was sending her on another mission, but that she would return when she could. James admitted to her that he needed time as well to figure out where the Winter Soldier's and Bucky Barnes's chapters end and where James Buchanan Barnes's life begins. Before she turns to leave, he pulls her close and kisses her with the promise that they will see each other again.
He doesn't know why he just did that.
But she smiles back at him and waves as she goes, and he allows himself a small measure of hope.
After all, that's how fairy tales begin.