Bitcoin is based on a mesh network. Rather than having a central server that all bitcoin wallets connect to, the wallets all connect to eachother. This is known as peer-to-peer networking and resembles a similar architecture to file sharing technologies such as BitTorrent. Peer-to-peer networking is highly resilient against censorship and control, since it has no single point of failure.
Have you any idea of what a "lay person" would make of these couple of lines?
It would mean absolutely nothing to them.Way way way overcomplicated.
That's in the "how does it work" section. That's more targeted at more tech savvy people who actually want to try to understand a bit more about what's going on behind the scenes. For most people, they would only read the first part.
I think most computer users below the age of 30 would have no problem understanding those 2 lines though.