What is the main idea of chapter 7 in Bud, Not Buddy?

I'm a bit unsure of what exactly you mean by main idea. The question might be asking for a general summary or a general theme. I will briefly go over both.  

Chapter seven begins with Bud going to the library. He is attempting to find Miss Hill. Bud searches the entire library, but he can't find her. Bud is forced to ask a different librarian where Miss Hill is. The librarian responds by saying, "Miss Hill? My goodness, hadn't you heard?" Bud immediately informs his readers of rule number 16.

If a Grown-up Ever Starts a Sentence by Saying "Haven't You Heard," Get Ready, 'Cause What's About to Come Out of Their Mouth Is Gonna Drop You Headfirst into a Boiling Tragedy.

It seems like the answer to "Haven't you heard" always has something to do with someone kicking the bucket.

Bud assumes that Miss Hill has died in some gruesome and tragic way. Fortunately that is not the case. Miss Hill is now a Mrs. She got married and moved to Chicago. The librarian helps Bud calculate how long it would take to walk there: too long. Disappointed, Bud leaves the library with no real plan of what to do next.

Thematically, chapter seven is about doors opening and closing. Earlier in the book, Bud told his readers what his mom said about metaphorical doors being closed and opened.

"And Bud, I want you always to remember, no matter how bad things look to you, no matter how dark the night, when one door closes, don't worry, because another door opens."

Miss Hill leaving Flint (and Bud) is a door being closed on Bud. He doesn't know where to go next, and Miss Hill can no longer help him find direction. It should feel like a depressing chapter ending, but it doesn't feel like that. That's because Bud ends the chapter by telling his readers that he knows another door is about to open. He is so confident in that hope that he falls right to sleep with little to no stress.

That library door closing after I walked out was the exact kind of door Momma had told me about. I knew that since it had closed the next one was about to open.

I went back under my tree and before I knew it I was asleep.

The chapter ends in a hopeful way.

Why is chapter 17 of Bud, Not Buddy so important?

Chapter 17 is important because this is when Bud begins to feel like he belongs. Bud is cleaning as the band sets up, and he’s pretending he’s in Twenty Thousand Leaks Under the Sea, which is how he remembers the title of the book he says his mother used to read to him. He says:

"It was a piece of cake! The bucket even had a thing on top of it that you could use to wring the mop out, and Herman E. Calloway didn’t even know how much fun I was having."

Working hard makes Bud feel like he deserves to be there, like he’s contributing just like one of the band members. He wants Herman to be proud of him, to see that he is strong and tough and should stay.

And then the band begins to play, and Bud is transfixed. It isn’t just music to him, it’s so much more than that, and when Steady Eddie starts to play, Herman says:

"He put his ax in his mouth and blew, but instead of the horn making music it seemed like Steady made it talk.”

Herman, Miss Thomas and Mr. Jimmy come up and Miss Thomas lets Bud know he did a great job cleaning and Mr. Jimmy agrees, calling him LaBone, his band nickname, further proving that he’s one of them. Herman grunts, which demonstrates his acceptance.

The three of them walk on stage and Bud becomes lost in their music, it resonates with him in a way that makes sense once you know he’s Herman’s grandson.

“The last thing you could hear was the rain from the Thug and the thunder from Herman E. Calloway getting farther and farther away, like the storm had gone and blowed itself over into the next county.”

This symbolizes that the storm of Bud’s life is moving on, blowing away into the distance.

It is amazing to me that chapter 17 can be described as important.  It is an important chapter, but it always shocks me how important it can be with how very little stuff actually happens in the chapter.  The story starts off with Bud cleaning tables and mopping floors.  He turns it into a sort of game in order for the work to not be monotonous.  The members slowly file in and begin to play their instruments in an informal jam session.  They are all impressed with Bud's hard work, and Bud is equally impressed by their playing.  That's it.  That's the entire chapter. 

But lack of action doesn't mean a text can't be pivotal.  Chapter 17 is important because it marks a change in attitudes for Bud and Herman. Until chapter 17, Bud has never really experienced music before.  He's so mesmerized by it that he can't find the words to express himself.  The chapter is important because it transforms many of Bud's preconceived notions about music and Herman. Additionally, the chapter transforms how the band views Bud.  

Why is chapter 17 of Bud, Not Buddy important?

In chapter seventeen, Bud witnesses Herman Calloway's band rehearse for the first time and is completely blown away by their awesome performance. The chapter begins with Bud mopping the floor and pretending that he is cleaning Captain Nemo's ship while The Dusky Devastators of the Depression begin organizing their instruments on stage. While Bud is mopping, he is distracted when the band begins to play and is captivated by the music. Bud compares the jazz performance to a thunderstorm as Thug uses his drum sticks to make a sound of splashing rain and Dirty Deed's piano makes it sound like the crashing of Niagara Falls.

Bud is so mesmerized by Steady Eddie's saxophone performance that he doesn't pay attention to Miss Thomas and Mr. Jimmy's compliments regarding his cleaning. He is then blown away when Miss Thomas begins to sing and believes that the band should be named after her. Once the rehearsal is over, Bud drops his broom and cannot stop clapping. Chapter seventeen is important because it highlights the magnetic, captivating nature of jazz music, which plays a significant role in the story. It also foreshadows Bud's love for music and desire to play with the band. While this chapter is not significant in regards to plot development, Curtis utilizes vivid imagery to emphasize the beauty and influence of jazz music.