Page numbers will vary by edition, but as the other answer states, the quote can be found at the end of chapter 11.
The key point is that throughout the novel, Atticus is trying to teach his children a new definition of courage. Part of this is through his reticence to let them know he is a sharpshooter until he has no choice but to display his great skill by killing a rabid dog with one shot. He wants them to understand, however, that there is no courage in such a God-given talent. This is what he means when he says that he doesn't want his children to get the idea that "courage is a man with a gun in his hand."
With the quote in question, he also wants the children to know that beneath her mean and nasty facade, Mrs. Dubose is a woman of great courage because she fights off a morphine addiction before she dies. It doesn't change anything, as she still dies, but it matters to her to die free of her addiction. She displays courage in facing the pain of withdrawal even though she is "licked before . . . [she] begin[s]." Courage, in other words, is doing the right thing because it is the right thing to do, not because there is a reward or "win" at the end.
This connects to Atticus's courage in mounting a real defense of Tom Robinson even though he too "is licked" before he begins. Like Mrs. Dubose, he does the right thing, all the way through to the end.