This is a difference between BLAKE3 and most other hash functions. In the usual arrangement ("Merkle–Damgård"), each block depends on the previous one, so the only way to verify some "slice" of the input is to re-hash the whole thing. But when you arrange the input into a tree shape (a "Merkle tree") instead, suddenly the right half of the tree does not depend on the left half until the very last step at the very top. If you give me the input to that last step, I can verify that it matches the root hash that I know, now I have the hashes ("chaining values") I'd need to verify either the left half or the right half without the other. Then I do our favorite trick in computer science, which is to recursively apply that same procedure all the way down, until I have an efficient "path" to whatever part of the tree I actually care about.

For more on this see Section 6.4 of our paper: https://docs.google.com/viewer?url=https://github.com/BLAKE3...

And the Bao repo: https://github.com/oconnor663/bao