The great challenges Jon faces in the novel are ones of identity, and after struggling to navigate these challenges he finally comes into a role he feels comfortable in. As he is frequently reminded, Jon is a bastard. He grew up with the Stark family, but he was never fully one of them, and the subsidiary role he played made him feel like a permanent outsider. When the novel begins, Jon is again an outsider. He pretends to join the wildlings but is actually still committed to the Night's Watch. But his time with the wildlings complicates his sense of where he belongs. To his great surprise, he finds that he fits in to a degree with the wildlings, who are themselves all outsiders in a sense living beyond the rule of the Iron Throne, and he genuinely likes a number of them. More troubling, he falls in love with Ygritte, a wildling woman. As a member of the Watch, he took a vow to forsake such relationships, but he eventually breaks his vow and carries on a romantic affair with her. John is left feeling torn between his loyalty to the Watch and his love for Ygritte and sympathy for the wildlings, but since they're marching to attack The Wall, he knows he will have to choose a side. He can remain with the wildlings and take on a new identity as one of them, or he can return to the Watch. Ultimately Jon escapse from the wildlings and informs the Watch of their intent to attack, but he still harbors feelings for Ygritte and sees the wildlings differently than he did before.
Jon later faces perhaps a more difficult decision after Stannis arrives and offers him rule of Winterfell. Growing up, Jon wanted desperately to be acknowledged as a Stark, but because he was a bastard, he was never considered a full member of the family. As a consequence he would also never be able to inherit Winterfell, even though he was the second oldest of the Stark children. Jon's status in his family was one of the motivating forces behind him joining the Night's Watch. It offered him basically a new family where he was equal to his brothers. Though he had some conflicts and didn't always get along with his new brothers, Jon was still able to make a place among them. Gradually he has shown himself a leader in the Watch, and during the battle with the wildlings, Jon demonstrates his ability in that role and wins yet more respect from his brothers. It's enough that, with a little clever strategizing from Sam, he is chosen their new Lord Commander. When Stannis offers Jon Winterfell, and the position he always dreamed of, he is essentially forced to choose an identity. He can be a Stark or a member of the Night's Watch. But as Jon weighs the decision, he recognizes that ruling Winterfell won't suddenly make him more of a Stark. He sees what he has found in the Night's Watch, and his decision to stay and serve as Lord Commander shows that he feels he has finally found his place and his identity there.