has slowly grown, and now it is so big that it is a central focus of his.  He plans to make his way across the entire state of Michigan in search of this man that he believes is his father:

The idea first got started when I was looking in my suitcase at one of the flyers showing Herman E. Calloway and his band. That was like the seed falling out of a tree and getting planted.

It started busting its head out of the dirt when me and the other boys at the Home were getting our nightly teasing from the biggest bully there, Billy Burns.

[...]

That little idea had gone and sneaked itself into being a mighty maple, tall enough that if I looked up at the top of it I'd get a crick in my neck, big enough for me to hang a climbing rope in, strong enough that I made up my mind to walk clean across the state of Michigan.

Bud's initially small idea has grown into a hugely motivating force.  It has grown into an impressive "tree," and that initially small idea is why Bud eventually winds up united with his grandfather. 

The answer to this question can be found in chapter 9. Technically speaking, Bud does not say that ideas are like trees. He says that ideas are like seeds.

IT'S FUNNY HOW IDEAS ARE, in a lot of ways they're just like seeds.

The idea and seed comparison comes up throughout the novel, but chapter 9 is the location where Bud explains the comparison. Bud says that both ideas and seeds start out small, and they both are capable of growing into something that is unfathomably larger than the original seed.

Both of them start real, real small and then . . . woop, zoop sloop . . . before you can say Jack Robinson they've gone and grown a lot bigger than you ever thought they could.

If you look at a great big maple tree it's hard to believe it started out as a little seed.

Bud goes on to explain that the idea of Calloway being his father started out just like that little maple seed. Bud explains that the initial seed of the idea was so small that it was likely to blow away with the first little breeze. It's fitting, then, that the idea itself began with a paper flyer of Calloway. That is an item that quite literally would blow away in any kind of breeze. Eventually, the idea that Calloway is his father is the only thing that fills Bud's entire field of vision. The idea is massive and powerful like a huge maple tree.

Once Bud finds Calloway and the rest of the band, he begins to feel accepted, and another seed gets planted, which quickly moves Bud from laughing to crying in an instant:

but sometime whilst I was sitting in the Sweet Pea another seed got to sprouting . . .

He has finally come home and found a loving family.