If the military invented the internet then what did Vinton Cerf do?

Cerf and Robert Kahn invented the Internet Protocol, and the Transmission Control Protocol, together known as TCP/IP. At that time, they both worked for the US Department of Defense.

The rest of this answer is about IP addressing and packet transmission, in case you were wondering.

Think of an IP address like a mailbox for every computer and website online.

When your computer sends out a message, it is broken up from one "letter" into many smaller "postcards" all headed for the same "mailbox" associated with another computer or website that you're sending to. Those "postcards" -- called packets -- may take 1,000 different routes to arrive at the destination where they are reassembled into your original message again.

Basically, before packets and IP addresses, there was just one computer or computer terminal "talking" to another over a dedicated connection -- think of that like a telephone without call waiting; just one on one. With routing, the packets can jump onto the "Information Superhighway" and take the most convenient route to get to a destination, flowing right along with other packets from other people, sharing circuit resources, until they get to where they're going.

(Yes, fellow nerds, I realize I simplified that like a crazy woman:)