There seems to be two stories going on, the one about Tom Robinson, the black man accused of raping a white woman, and then the story about the kids.
Do the two stories have anything to do with each other?
Umm. Yes, they do. Why do you think Scout was being chased through the woods during the climax?
Just rent the video if it’s easier.
The book is about courage.
I think it’s to be expected if you’ve made it this far, but there are potential spoilers to this book in this post. If you’ve somehow never read the book but were curious enough to open this thread and for some reason do not want to be “spoiled” then please turn away right now. 
Do the two stories have anything to do with each other? Maybe I don’t quite understand what story about the kids you mean. The primary storyline about the kids was to demonstrate how they are being raised by their noble father and how he is teaching them right from wrong as he raises them and teaching them how to treat other people, including people who are racially or otherwise different from them. The storyline about Tom Robinson is the primary example of their father living out what he is teaching them. He is not popular because of his willingness to take the case and defend Tom Robinson as an equal and as a man. This unpopularity is what leads to the climactic chase scene when the kids are being terrorized by a narrow-minded man who thinks little of their father because of the way he defends Tom Robinson.
Does that help? Or is there some other storyline involving the kids that you were talking about and that I don’t remember off the top of my head?
Okay, spoilers ahead, although I assume anyone who opened this thread is interested in the actual stuff going on in the book.
Yes, the two stories are related. Granted, the two story arcs are not especially related, until the final scene with Scout in the ham costume (is that the best or what? she’s a ham!). So we’ve got two things going on here, the trial and the adventures of the kids. They are related because the trial is addressing issues of justice, revenge, conviction, convention, race and class. These are pretty much the same issues Scout encounters, although her experiences are that of a child. For just about everything going on with the adults in the town, a related issue is happening with the kids.
It’s a story about an adult thing experienced by children.
Consider the title: Remember when Atticus gave the rifle to Jem for Christmas and told him that he could shoot other birds but, "it's a sin to kill a mockingbird"? Miss Maudie later explains that mockingbirds don't bother people at all but simply spend their days making beautiful music.
The mockingbird becomes a symbol for innocence. Tom Robinson is certainly a 'mockingbird', he's obviously innocent of the crime, and the book allows us to see how they respond to their first experience of the sin of innocence destroyed.
Jem doesn't deal with it well at all. After the trial he becomes cynical and short-tempered.
Scout, perhaps because she's so young, isn't as negatively affected. She is also the one who finally gets to meet Boo Radley and discovers that the monster is actually another 'mockingbird'. This is a big step towards understanding what Atticus has patiently been trying to teach her all along: We're all mockingbirds, or at least we all started out that way.
"Atticus, he was real nice."
"Most people are, honey, when you finally see them."Sorry I wasn’t more specific. The thing that really confused me was the whole Boo Radley thing. He seems to have been an important part of the story, but I don’t see how he ties in with the Tom Robinson part of the story.
And yes, I have read the entire book, so don’t worry about spoiling it for me.
Boo Radley ties in because, as the post above noted, he is also like a mockingbird – innocent and not bothering anyone. The “adult” storyline is their father showing them how Tom Robinson was innocent, didn’t bother anyone, just tried to help others, and was wrongly judged by society. The “children” storyline is that the children (especially Scout) are able to take what their father has taught them and experience and understand it as it applies equally to Boo Radley.
Hope that helps you.
Like Roadwalker says, the book is about courage.
SPOILER ALERT:
Boo Radley shows his courage at the end of the book, when he rescues the kids.
It might be a stretch, but I think Boo Radley was intended to represent good white Southerners who knew that racism was wrong but who were too timid to do anything about it. In the end, Boo overcomes his timidity long enough to confront the racist cracker who attacks the kids. Like I said, might be a stretch.