A handily written, succinct history of the Internet from Marcus Kazmierczak had this to say on the nascent begginings of the web:
...The early 1960's, in the middle of the cold war, was possibly the closest this world has ever been to nuclear annihilation. The US Department of Defense wanted a network of computers which would allow them to continue to communicate even if partially damaged... Enter Paul Baran and his colleagues at the Rand Corporation... (who) came up with one of the crucial ideas behind the Internet, packets. They did not call them packets, and did not develop the technology, but they had the idea.
The idea was to break up the transmissions into a discrete number of pieces. These pieces, each of which contain information on where it is supposed to go, would then be sent out through a network of phone lines connecting numerous computers. Since each piece contained the directions on where it was supposed to go, it did not matter what route it took to get there, and thus did not matter if some computers were down in between. The packets once arriving at their destination are reassembled into the original transmission.
Fascinating stuff that someone in my position probably should have been aware of by now. It's amazing how much we still have to learn about the things we use every day. I didn't actually realize that my corporation was already producing great ideas more than a decade prior to my birth :)