Burris Ewell only goes to school on the first day and that she could follow a similar plan. After explaining the Ewell family to Scout, Atticus offers her a compromise. He says, "If you'll concede the necessity of going to school, we'll go on reading every night just as we always have." Scout accepts the offer.

The compromise offered by Atticus shows that he is willing to listen to Scout's side of a story. The compromise also shows that he is willing to bend the rules a little when it comes to doing what he feels is best for his children. He teaches Scout to respect Miss Caroline and to understand things from her point of view, but he knows that his reading time with Scout is important to her.

In chapter 14, Jem tells Scout to stop antagonizing her aunt Alexandra because it just causes more contention in the house. Jem even says that he will spank her if she does it again. This drives Scout to the point of physically lashing out at Jem and Atticus goes in to break it up. He asks who started it and Scout says the following:

"Jem did. He was tryin' to tell me what to do. I don't have to mind him now, do I?" (138).

Poor Scout. She has to obey so many people in her life: Calpurnia, Atticus, Aunt Alexandra, and now Jem! Life is pretty crazy since the trial of Tom Robinson is just around the corner. Jem was trying to help Scout not cause any other trouble, but he lacks the parental experience and authority to do it correctly. Atticus, being the compassionate and wise father that he is has the best response for Scout:

"Let's leave it at this: you mind Jem whenever he can make you. Fair enough?"(138).

Could it get any more ambiguous than that? Does it seem that Atticus is saying that if Jem can physically make her obey, then she will have to? Or, is he simply distracting Scout so it can be called up for discussion at another time? Either way, it leaves the situation up to Jem and Scout to resolve on their own when the time comes. Ultimately though, the compromise is that Atticus won't actually say Scout must mind Jem unless Jem can figure out a way make her mind. 

I'm going to assume by your one word question that you are referring to the compromise made between Scout and Atticus in Chapter 3 of To Kill a Mockingbird. Scout had had a terrible first day at school after running afoul of her first grade teacher, the inexperienced newcomer, Miss Caroline. Among Miss Caroline's complaints was that Atticus was not a qualified teacher, and she demanded that he stop reading to Scout. Scout decided that it would be best if she quit school; she could learn everything she needed at home, taught by Atticus and Calpurnia, she believed. But Atticus had another idea.

"Do you know what a compromise is?" he asked.

Scout responded:

"Bending the law?"

Atticus explained that it was "an agreement reached by mutual concessions." When he proposed that Scout return to school if they both agreed to continue their nightly reading--without Miss Caroline's knowledge--Scout accepted the "bargain."

In Chapter 14 of To Kill a Mockingbird, Scout becomes overwhelmed with all of the people in her life who are telling her what to do. Aunt Alexandra has recently moved in with them, and it is difficult for Scout to mind this new woman who openly disapproves of her. To add salt to the wound, Jem attempts to tell her what to do in order to bring peace to the household. This doesn't sit right with Scout because she sees Jem as her equal, not her superior. As a result, Scout provokes him into a fistfight that Atticus has to break up. Atticus asks the children who started the fight and Scout blames Jem because he was telling her what to do. She asks her father if she has to mind Jem from then on, too. Atticus makes the following compromise:

"Let's leave it at this: you mind Jem whenever he can make you. Fair enough?" (138).

This seems to satisfy Scout because it gives her some support for a time that Jem might tell her what to do in the future. In fact, Scout uses this during the Tom Robinson trial when Jem tells her to go home. Scout responds by saying the following:

"'You gotta make me first,' I said, remembering Atticus's blessed dictum. Jem scowled furiously at me . . ." (173).

Therefore, the compromise is that whenever Jem bosses Scout around, she doesn't have to obey him unless he can make her obey.

Atticus agrees with Scout that they will still read together. 

Atticus was in the habit of reading to Scout, following the words with his finger.  Because of this, and because of Calpurnia's giving Scout sentences to copy when she wanted to keep her busy, Scout is already able to read fluently when she starts school.  

The young, inexperienced teacher is horrified that Scout has been taught to read at home.  (She assumes that Scout's father used the wrong methods to teach her.)  She tells Scout not to read outside of school anymore, and she, the teacher, will try to "undo the damage."

Scout does not want to give up one of her favorite pastimes, so she mounts a campaign to get Atticus to let her stop attending school.  When Atticus finds out that one of Scout's main concerns is that she won't be allowed to read outside of school, he tells Scout that he'll still let her read at home as long as she agrees to go to school.