Before Shannon, nobody could say how much a message actually contained. In one 1948 paper he defined the bit, worked out how much you can push through a noisy channel, and showed that you can send data almost perfectly over a bad line if you encode it well. Every phone call, hard drive and Wi-Fi signal since then has been an engineering footnote to that paper.
A decade earlier, as a master's student, he had noticed that the switching circuits in telephone exchanges behaved like Boolean algebra. That observation is basically why computers are built out of logic gates.
Then he mostly wandered off. He juggled, rode a unicycle through the halls of Bell Labs, built a mechanical mouse that could learn a maze, and made a machine whose only job was to switch itself off. He didn't seem to care much about credit or about staying in one field.