A big, sweet, old woman, Miss Emma has taken care of Jefferson his whole life as his godmother (or as they say in Louisiana, nannan). Before that she was the cook and housekeeper on a plantation until she had saved enough to get by without working in that kitchen.
We don't know much about her life other than that, but what we do see of her is her dedication to Jefferson. Our first glimpse of her is at the trial:
Either I sat behind my aunt and his godmother or I sat beside them. Both are large women, but his godmother is larger. She is of average height, five four, five five, but weighs nearly two hundred pounds. [. . .] She never got up once to get water or go to the bathroom down in the basement. She just sat there staring at the boy's clean-cropped head where he sat at the front table with his lawyer. (1.1)
Miss Emma's physical stature combines with her behavior to give us the impression that she is an unmovable rock. She might not be strong enough to sway the court's decision or to protect Jefferson from his fate, but she is strong enough to stay right where she is and support him. And that, in our humble opinions, is freaking awesome.
In the novel, the sort of unwavering faith that Miss Emma personifies, acts as an important contrast to Grant's flimsy faith in humanity. Miss Emma basically has no good reason to hope for anything—she's old, poor, and is losing her only family member unfairly. Life has dealt Miss Emma a bad card, to be sure. But she remains steadfast, hoping that at least one thing can change before she dies.
Miss Emma is strong, because she is able to keep on keeping on even under the hardest circumstances. She can also be a little bit of a trickster, and she plays sick when she wants Grant to go alone to visit her godson:
Miss Emma [. . .] had on two sweaters, a black one over a green one. She had some kind of rag, possibly a baby's diaper, tied around her head. [. . .] I had the feeling that Miss Emma was not nearly as sick as she was pretending to be. For one thing, I had seen her that morning picking up chips in the yard, and she didn't look sick at all. And now I could smell fried chicken and baked potato, and I knew she could not have done all that if she was dying. (10.12)
So Grant knows that Miss Emma is playing hooky from visiting the jail and that she is perfectly capable of leaving if she was able to do yard work and cook. He just takes it as another irritating thing that she and his aunt do to ruin his life. But we, the readers, can look past the annoyance and try and figure out why Miss Emma does what she does.
Perhaps Grant is right and it is a big conspiracy to get him to the courthouse alone. We know that Miss Emma doesn't stop visiting Jefferson; she just pushes Grant to visit him without her company. So she must be motivated to have the two men visit one on one without her interrupting.
The old nannan is not a very powerful figure, traditionally speaking: she has no money, she is old and weak, she does not have much of a family to protect her, and she really is on her own in the world. However, she can influence events by just being still… she can't physically force Grant to do what she wants, so she has to manipulate the situation. She has to get him into the habit of going and then be still and let him go on his own.
Miss Emma's overall goal is for Jefferson to stand up like a man before he dies, and she truly believes that Grant is the one who can help him do it. That's why she steps out of the picture by playing sick: to give the two men room to grow.
In the novel, Miss Emma really works as a sort of a motor. No, not the vroom-vroom kind: she is more of a quiet but insistent plot motor. She's very much in the right place at the right time, plotwise. She's Grant's aunt's friend, so that's how she influences Grant. She worked for Henri Pichot for years, which gives her the clout to speak to Pichot's brother-in-law, the sheriff.
Even though, like we mentioned above, she isn't the most powerful person in her community, she's clever enough to manipulate people into doing what she wants when it really matters. She may not move the community, but boy oh boy does she move the plot of A Lesson Before Dying.
Another really important aspect of Miss Emma's power is that she's the one who means enough to Jefferson to help him stand up at the end of his life. His last words, "Tell Nannan I walked" (31.54), are dedicated to her, which shows just how important she is to getting this story moving.