No, I'm not talking about web servers on the internet. I'm talking about the network itself.
Basically you set up a channel for which packets which are broadcast are returned to their source (think IRC here: What you type eventually winds up on your screen in the channel your talking on).
Thus your able to put the data into the network, forget it, and retrieve it when it makes the round trip. It's not actually 'stored' anywhere retrieveable... it just uses the latency of the network to keep the data alive for a period of time.
There's even flags in TCP which he outlines which turn virtually any TCP stack running on any machine (windows and unix alike) into short-term data stores.
The whole thing is best compared to Juggling (as the paper points out): At any given time, you only hold some (or none) of the data, and some of the data is 'in the air'. If you just keep juggling the data, it can be 'stored' on the network itself.
Anyone ever read past the first book of Enders Game?
Remember how the AI came about in that?