Okay, I think I get it.

A hash with N initial zero bits corresponds to a probability that something close to 2^N total hashes have been performed, because, on average that's how many hashes it takes to get one with N initial zero bits.

Within the same set of hashes, you "expect" to find around two hashes with N-1 initial zero bits.  Each of these corresponds to a probability that something close to 2^(N-1) hashes have been performed.  If you have two of them, that adds up to 2^N total hashes (same as the work presented by the parent node).  If you have only one, though, your estimate is lowered (by half) and if you have five your estimate is increased (multiply by 5/2). 

Each of these hashes with N-1 initial zero bits is then expected to dominate around two hashes with N-2 initial zero bits. Meaning, if you had two at the N-1 level, you expect around four, and if you had five at the N-1 level, you expect around ten.  And each of these N-2 hashes represents around 2^(N-2) total hashes.  If you expected ten and you find seven, you lower your estimate (multiply by 7/10).  If you expected four and you found seven, you'd raise your estimate (multiply by 7/4). 

And so on, so the more of the "high nodes" on this hash tree you process, the better your estimate gets.  The law of large numbers means each "generation" verified downward from the root of the tree will lead to smaller and smaller adjustments to the estimate, and you probably have a very good idea (within 1%) of the total work by the time you've found the ~50 best hashes. 

This procedure can be carried down to the level of difficulty as of the time the block was mined, below which there's no information so you just have to treat your estimate on the individual blocks as the "truth" or as close as you can get.

So this gives you a way of getting a rapid estimate of the total amount of hashing work that went into a particular blockchain, or into the portion of it discovered since the blockchain fork. 

Okay, I see the value there.

It's also interesting that you could do the same kind of linking on any metric; for example the amount of coin age destroyed by a given block, if that were your measure of "best chain" instead of the number of hashes.