Abe's probably most important relationship is with his mom, who helps shape him when she's alive, when she's dying, and when she's dead. Good job, Mom.
When she's alive, Nancy helps encourage Abe's education by reading to him, which was a pretty rare thing in the pre-Kindle Kentucky wilderness (1.27). She encourages his curiosity and even teaches him how to read for himself, so he can continue his education on his own.
And when she's dying, Nancy Hanks Lincoln gives her son one deathbed command: "Live" (1.67). So when Abe is suffering from his deepest depressions, he remembers this command and perseveres like the good son he is. After Ann Rutledge dies, it is only the memory of his mother's command to live that keeps Abe from killing himself:
I could not…
I could not fail her. I threw the weapon on the floor and wept […]. (6.110-112)
Finally, when she dies, Nancy provides some pretty heavy motivation for Abe. Whenever he meets vampires, he remembers that these are the creatures that killed his mother. When he figures out that Henry is a vampire, Abe thinks "my sworn enemy! my mother's murderer!" (3.63).
And there you have it, Shmoopers: Nancy in a nutshell. In her short appearance in the book, she makes sure Abe can teach himself, will not kill himself no matter how hard it gets, and gives his life direction by giving him a goal: the extermination of all American vampires.
That's really all we can ask one mom to do.