Atticus tells Scout this so that she will realize that his choice to defend Tom Robinson is a moral choice.
Atticus says that there is a case in every lawyer’s career that “affects him personally” (ch 9, p. 100). His point is that he takes the case seriously because it requires him to make a moral decision. He has to stand up not just for Tom Robinson, but against the town. He has to make the choice to do what he thinks is right.
“Simply because we were licked a hundred years before we started is no reason for us not to try to win,” Atticus said. (ch 9, p. 101)
Atticus is telling Scout this so that she will learn a life lesson. It is a person’s responsibility to stand up for what he or she believes in. You need to stand by your choice, if you think it is right, even if it is not the most popular choice. This is the strongest lesson that Atticus teaches Scout. He leads by example, showing her that it is important for a person to do the right thing. This is the only way that racism can be overcome.
It is also significant because "Atticus represents the moral backbone of the town of Maycomb" (enotes, character analysis). By standing up for what he feels is right, he is showing the town what is right. Ultimately this does make a difference, because the jury does at least consider Tom Robinson's potential innocence.
To read more character analysis, see here: http://www.enotes.com/to-kill-a-mockingbird/character-analysis
To read a summary of this chapter, see here: http://www.enotes.com/to-kill-a-mockingbird/chapter-9-summary-analysis
To understand Atticus' statement, you have to know what kind of person he is, and the sort of values he has. He very strongly believes that Tom Robinson is a victim of bigotry. He believes that Tom is innocent of commiting any crime, and that the real reason Tom is being accused has to do with Tom's skin color. Atticus' statement means that he intends to stand by Tom no matter what, because he can't live with himself if he doesn't stand for what's morally right, even if everybody else in town disagrees with him.
What Atticus is really talking about is being able to live with your own conscience. Atticus would lose his self-respect if he went along with the bigotry and hypocrisy of the town. The townspeople would like Atticus better, but Atticus would not like himself. This passage illustrates the importance of self-respect. Self-respect is a universal need. Without it, a person feels shame and disgrace.
If he didnt respect others then people wouldnt respect him.