Jessie was the loving wife of Max Rockatansky and the mother of their toddler son - Sprog. She was a keen saxophonist and loving wife and mother to her husband and son and was one of the more gentler of people Max encountered during his life. Not much is revealed about their marriage prior to the events in Mad Max.
Her first appearance is the night following Nightrider's death, having played a piece on her saxophone for her husband and son, a news report on the television set informs of Max's killing as she dries his hair after a long bath. She asks who Nightrider was, to which Max replies: "Just another Gloryroader," to which she seems unfazed. It seems such acts by Max were common to her and that they resulted in little worry from her.
However the next morning she expresses a considerable amount of depression when Max states he has to get going to work and a striking loneliness seems apparent. When she waves him off she shows her ability to use sign language - commenting that she's crazy about Max.
After Goose's fatal accident, Max decides to have a break from the MFP and the entire family take a vacation up north at May's Farm. Having gotten a bad tyre, Max pulls in at a local garage to have it mended. Meanwhile, Jessie and Sprog drive down to the nearby beach to get icecreams. When there, she is confronted by some of Max's current adversaries from Toecutter's motorcycle gang and no other than Toecutter himself. Having been briefly molested, she manages to escape and drive back up to the repair garage where she picks up her husband and flees back onto the outback roads.
Having long lost the Toecutter gang, Jessie, Max and Sprog eventually make it to May's Farm which seemed to be their destination from the start. Finally being able to relax, the couple and infant are greeted by May, (who could be a family friend or relative - it's not specified) and what appears to be her mentally challenged son. However as Jessie relaxed at the beach, she's once more pursued by the Toecutter gang who have appeared to have followed the family.
Eventually making it back to the house with May thinking once more to have lost the bikers, Max broke away to hunt them down with May's son, whilst May and Jessie took a breather back at the farm. However trouble arose once more as Jessie realised she couldn't recall where she'd placed Sprog. Desperately searching the farmyard, she met eyes with Toecutter once again who had taken Sprog hostage in demand for the hand she'd ripped from a member of his gang - Cundalini, who's hand was accidentally ripped from him as Jessie and Sprog escaped from the beach upon her first encounter with Toecutter.
Opportunity then came to pass into Jessie's favour as May ushered the gang into a pantry with the threat of her rifle. Taking Sprog with them, May, Jessie and Sprog drove away from the farm as fast as they could only for their car's radiator to blow - leaving them helpless in the middle of the road. As May told Jessie to run with Sprog on foot, she lifted her rifle to take out whatever gang members she could as they passed. Unfortunately missing every single one, the gang drive past May and toward the fleeing Jessie.
In a violent and merciless blur, it wasn't long before Toecutter ran her and her infant child down.
Max ran to the scene only to find his son dead and Jessie in critical condition. This event pushes Max over the edge and permanently traumatizes him. It solidifies his solitary attitude, philosophy and personality in the the remaining movies, Mad Max 2: Road Warrior, Mad Max: Beyond Thunderdome and Mad Max: Fury Road
Even though it is not clear if Jessie dies or lives in a vegetative state for the remainder of Mad Max, the intro to Mad Max 2 shows Max walking away from two graves, signifying that both his infant son and wife had died.
First and foremost, Jessie was a caring and loving wife to Max and mother to Sprog. However, she showed a range of other abilities. Jessie had a musical ear, and appeared to be a talented saxophonist. Jessie was also capable of using a variant of sign language, something that she shared with Max. Why she was able to use signing was not specified.