In childhood, Jane’s cousin Eliza is just another nasty member of the Reed family; as an adult, she becomes more and more prim, proper, and repressed as she jealously watches all the boys flock to her sister Georgiana. Eventually, she’s turned herself into a robot, with every fifteen-minute period of every day of her life scheduled and organized, and no friendships or romances or loving relationships of any kind. When her mother dies, she moves to France and becomes a nun.
The novel wants us to think about her as pretty wrongheaded in this decision; instead of dealing with her jealousy and disappointment, she tries to cut emotion entirely out of her life and spend her whole life being blank and detached. Hmm, does that sound like any other characters we meet later in the novel? Yep, Eliza Reed prepares us (and Jane!) for St. John Rivers.
One major difference: one of Eliza’s problems is that she doesn’t become a nun because she feels called to serve God, but because she wants to get away from the world. St. John at least has a genuine "calling" to be a missionary.