How does Scout react when Atticus explains to her why he has decided to defend Tom Robinson?I know Atticus explains he does it because he wouldn't...

Scout is young and doesn't understand everything her
father is telling her--yet.  In fact, Harper Lee often uses Scout's youthful ignorance
as an opportunity for the adults to explain what she wants the readers to hear about
prejudice and hate and other harmful stereotypes.

In this
case, Atticus does explain his position, as you noted.  He tells Scout, in answer to her
question, that they will probably not win this case.  He then asks her for one thing--to
keep her cool and not pick a fight over this matter.  Her reaction is pretty basic,
considering she really doesn't understand what her father is asking her to do--to accept
that others will be ignorant and cruel and hurtful because they have not learned
better.  She is capable of being the bigger person, and that's what he asks of her. She
promises. 

She tries, she really does. but when her cousin
Francis calls her father names she simply has to haul off and whack him--prompting
Atticus to let Scout overhear a conversation in which he admits his fears for the summer
ahead and his hope that his children will come to him first rather than try to fight. 
She doesn't make another promise, but she does better the next time she is
tempted.