The reason Mrs. Dubose would lengthen Jem's reading sessions by two minutes each day was to acclimate her body to not using morphine every two hours until she was able to conquer her addiction completely.

In chapter 11, Jem and Scout walk by Mrs. Henry Lafayette Dubose's home on their way to the store and listen as she begins calling Atticus derogatory names. Jem tries his best to ignore Mrs. Dubose but loses his temper after she calls Atticus a "nigger-lover." On their way home from the store, Jem takes Scout's new baton and proceeds to destroy Mrs. Dubose's camellia bush before he snaps Scout's baton over his knee.

Later that evening, Atticus makes Jem apologize to Mrs. Dubose. When Jem comes home from Mrs. Dubose's home, he tells Atticus that she requested that he read to her for two hours every weekday and Saturday afternoon for an entire month. Atticus ends up making Jem read to Mrs. Dubose daily, and Scout tags along. When Jem first begins reading to Mrs. Dubose, she nods off early into their sessions, and the children have to leave when her alarm goes off. As the month progresses, Mrs. Dubose stays awake for longer periods of time and their reading sessions become longer. Scout says,

"It suddenly came to me that each day we had been staying a little longer at Mrs. Dubose’s, that the alarm clock went off a few minutes later every day, and that she was well into one of her fits by the time it sounded" (Lee, 113).

After Mrs. Dubose passes away, Atticus explains to the children that Mrs. Dubose was addicted to morphine and was determined to conquer her addiction. Jem's reading occupied her mind between morphine doses until she was able to quit using morphine altogether.

Mrs. Dubose is a morphine addict. She knows she is about to die. She wants to die free from addiction to that drug. However, because of her great pain, this is difficult to do. The kids coming to read to her is one way she can at the very least be distracted and hope that she can go longer in between doses. Most addicts know that this begins the process of weaning themselves off of their addiction, put more time in between consumption moments.

For the kids, this just seemed mean at the time. They didn't understand what she was really working towards. Once she does pass, Atticus reveals to them her great courage and what she was trying to do in the end of chapter 11.