Lady Jessica is Paul's mother and the Bene Gesserit lover of Duke Leto. She is perhaps the second most important character in the story, and considering the long list of characters in this story, that's saying something. Like Paul, Jessica's adventure through Dune is also a coming-of-age story. Yeah, we know that coming-of-age stories are usually reserved for children becoming adults, for or senior citizens deciding being old isn't so bad. But with Jessica things go a little differently. Here's why.
When we first meet Jessica, she's technically a mother. Heck, Paul's fifteen years old, so she's been a mother for a while now. But Jessica doesn't have much in the way of motherly instincts yet.
When the Reverend Mother comes to test Paul, we see Jessica act very submissively toward the older lady. The Reverend Mother treats Jessica like a "serving wench" (1.61), and Jessica feels like a "little girl again" when around her (3.43). She also serves the Bene Gesserit mission of finding the Kwisatz Haderach, and for this reason, she lets the Reverend Mother test Paul with the gom jabbar.
But we also see Jessica act the part of an independent woman and mother. She willingly disobeys the Bene Gesserit order to have a girl, giving birth to Paul instead. She also states she will "shield [Paul] as well as [she's] able" (3.33).
Between these two examples, we find a confused Jessica at the beginning of the novel. On the one hand, she's still a little girl being ordered around by her elders. On the other hand, she is starting to develop the motherly instincts of nurturing support and protectiveness that will develop in her as the novel progress.
In the second half of the novel, Jessica and Paul must both find their place amongst the Fremen. For Jessica, this means passing the test to become their Reverend Mother. The test requires her to drink the Water of Life, consuming the Other Memory in the process. Afterward, Jessica enters the role of the goddess mother for the Fremen.
As Stilgar notes, the Reverend Mother's role is to "teach [and] maintain the strength of God" (32.73). But it's more than that. The Other Memory grants Jessica the genetic memory of all the Fremen mothers who came before her. Freaky as that may sound, it basically means she becomes the guardian of the Fremen history and culture. It will be her job to nurture and support their culture and religious beliefs in the same way a mother nurtures and supports a child.
By the final third of the novel, Jessica has finally grown up—took her long enough. She's been the Reverend Mother of the Fremen for some time and has been fully accepted into their culture. She's also very defensive of her daughter, Alia, whom she understands better than anyone else, having been present when the girl came of consciousness in the womb.
But the major change in Jessica is shown in how she relates to the Reverend Mother Gaius Helen Mohiam and Paul. At the novel's end, the Reverend Mother tries to command Jessica to silence Paul. Jessica responds, "Silence him yourself," showing that she has grown from the scared little girl of the story's beginning. She's now an equal with the Reverend Mother, and she knows it. Good for you, Jessica.
She also shows a decidedly different approach to Paul's wellbeing. Earlier, Jessica was worried about grooming Paul for the role of Kwisatz Haderach, as well for the role of Duke of a noble house. The first required intense mental and physical training; the second meant that Paul would have to marry into another royal house.
But when it comes time for Paul to marry Irulan, Jessica begs her son to not "make the mistake [his] father made" (48.76). Jessica originally wanted the world for her son, but now she has come into her own as mother. She wants only her son's happiness, and she believes that path to lie in marriage to Chani.
Over the course of the novel, we see Jessica maturing into her role as the mother archetype. In the first role, she's strong enough to stand up to others, and in the second role, she's strong enough to stand up to tradition and custom. In both cases, she does so for those she loves and wishes to protect and support.
And if that's not a momma bear, then we don't know what is.