This would be a hash of an index file that describes the data, broken into small chunks. Now your client goes back onto the network and finds the cheapest way to retrieve all these chunks. You could set a default, "5 cents per GB" that you're willing to pay.
Servers could monitor the network and see what's being requested often, and pay to download (and re-serve) these chunks themselves in the hopes of profiting. When files become rare, servers could charge a premium.
Bitcoin is not a micropayment system, so paying per chunk would be expensive. You could pre-pay, say 1GB at a time at first, and slowly build up a trusted reputation where you only pay afterwards (by reusing a bitcoin address as your "identity" that you always send from). You'd work out a "contract" (signed with your sending address), give it to the server, and if you skip out on paying they could use it as proof of nonpayment which they would share with other servers. (Maybe all servers have a blacklist file they share for free). They could try to send you bogus data, but since you can verify by-the-chunk you wouldn't request more chunks from them once you've received a piece that fails a hash.
Once you've got this network in place, you could build any of the things the author in this link is describing. My hope, a Usenet 2.0 style protocol. The whole thing is very exciting. But first you need a simple, generic, data-for-bitcoin network.
Everything I've seen so far in the bitcoin/storage area (maidsafe, storj) sounds overly complicated and downright scammy. I don't want to back up my data to a p2p network. I don't want to have to purchase a new altcoin to use your network. I just want to, for starters, type "serve [file]" or "fetch [hash]" on the CLI and have it all magically work behind the scenes. First place I'd see this taking off is sharing porn - yay! From there, after time, it could become the backbone of "web 3.0".