Not much is known about the mysterious Planetary Connection. Various hints were given to it in Season 3, but it was fully explained in The Connection.
Azmuth's first Omnitrix prototype was a wireless device, but very short-range compared to the current one. So he built recievers/broadcasters in the core of every planet in the galaxy. (It became obsolete before it could expand to other galaxies.) The Omnitrix prototype would draw the DNA from Primus, through a chain made up of the recievers, and reach the Omnitrix for the user to transform. Eventually it was shut down and the web it made was dissolved. But glitches and viruses developed in the stations, so special Plumbers would guard the entrances. According to Azmuth, if the Connection was reactivated, the glitches and viruses would combine to create an energy wave that would destroy the universe. Unlike the Omnitrix's SDM, it would spread through crosstime and the different realities, destroying absolutely everything.
Paparo plans to reactivate it himself. Because of his insanity developed from hatred for Ben for ruining his original plan, he wants to destroy him and everyone and everything else, including himself. One of the requirements to reactivate it is a large amount of Codon Stream DNA, and that's why he had Zeno steal a lot. It was later recovered, though.
Earth's station was seen briefly at the end of Return of the Nanochips, where a man, presumably Paparo, was walking through with some Nanochips. It was the only one to be completed.