Here's a quick overview of computer history. I taught this lesson in a single one hour session, but you can explore further in the links and probably expand this into an entire semester if you wanted.
1801 Joseph-Marie Jacquard exhibits his Jackquard Loom, which uses punched cards to control a sequence of operations to make different fabric patterns. Jacquard is credited as the inventor of the first programmable machine. His loom is not a computer, but this loom is an important predecessor in the development of programmable computers.
1837 Charles Babbage describes his proposal for a programmable Analytical Engine, which can be programmed with punch cards to solve mathematical equations. Mathematician Ada Lovelance worked with Babbage and is credited as the first computer programmer. In 1979, the computer language Ada was named in her honor. Babbage was never able to build a working Analytical Engine.
1890 Herman Hollerith develops tabulating machines that uses punch cards to complete the U.S. census in record time. Hollerith founds the "Tabulating Machine Company" which, after various mergers, eventually becomes IBM.
1936 British mathemetician Alan Turing describes the Turing Machine, an important step in the development of computer science theory. The Turing Machine is used to help computer scientists model processing behavior and algorithms.
1937 Bell Labs researcher George Stibitz creates a calculator he calls the "Model K" which used Boolean logic mechanical relays. (We'll cover Boolean logic later)
1939 University of Iowa researchers pioneer important computing concepts with the Atanasoff Berry Computer, including binary arithmetic and electronic switching.
1940s Computer hardware development explodes due to World War 2. Norden bomb sight and artillery fire control are some examples of mechanical computers used in warfare. The British built 10 Colossus computer -- large, building sized electronic digital computers -- to break German codes. They used thousands of vacuum tubes to perform calculations, and data was input using paper tape with holes punched into them, which controlled the movement of metal wheels with pins on them.
1943 ENIAC -- the first general purpose electronic computer.
1945 Mathemetician John von Neumann describes the von Neumann architecture. This describes your basic stored program computer with an arithmetic unit, control unit, a common memory to store data and programming, input and output, and external storage. Instructions and data are fetched via a common bus (or data transfer circuit). von Neumann's store program architecture was an advancement over earlier program controlled computers, which were programmed by hard wiring the instructions as part of the computer architecture.
1950s - first commercial computers developed.