Here's my attempt at an explanation, after reading the article.
Most companies' networks have edge routers (which sit at the points where they connect to other networks) and core routers (which manage the flow of traffic inside the network. All these routers basically use a standard protocol called BGP (Border Gateway Protocol) which is defined by RFC 4271.
However, BGP was still designed from the view of individual machines making routing decisions and announcing routes to each other that collectively make up the whole Internet. This helps the Internet as a whole be quite resilient – if one network goes down, there are still ways to route traffic through to other networks. Also, since the protocol is standard, you can swap out one vendor's gear for another at will (in theory anyway) as long as you know how to configure it correctly.
But this leads to some inefficiency – for instance, it is very hard to say that a path with fewer hops will lead to lower latency. What Google seems to have done is to make their edge routers into one single "intelligent" network, where the edge routers don't make routing decisions on their own, but feed their data into a central server. This central server can then say stuff like "My peering router in NYC seems to be under heavy load, let me redirect some of my traffic to NYC destinations through the NJ datacenter instead", or something to that effect; while still doing the correct BGP announcements from the point of view of Level3 or whoever is peering.
In short, they built their internal network from the ground up since they are so big they can afford to build custom routing gear instead of using the standard off-the-shelf, standardized setup that a small or medium-sized company uses. The network consisting of their custom edge routers (all the green blobs) together is called Espresso and represented by a light grey circle.