Bitcoin is confusing at first glance because so many problems are solved using just a few ideas. If you think about it long enough, it is quite elegant.
The busy-work of finding a block hash that is "small enough" solves a couple of problems:
First, by making it hard to create coins so they are artificially scarce. That is really important; if it was easy to create gazillions of bitcoins we'd all have gazillions of bitcoins that were worth nothing.
Second, it solves the double-spending problem-- the computer that solves the busy-work problem first gets to decide which transactions are "THE" transactions, and which ones are invalid (because you're trying to spend coins you've already spent).