The punched card actually predates computers considerably, originating in 1801 as a control device for Jacquard looms. Such cards were also used as an input method for the primitive calculating machines of the late 19th century.
The version by Herman Hollerith, patented on June 8, 1887 and used with mechanical tabulating machines in the 1890 U.S. Census, was a piece of cardboard about 90 mm by 215 mm, with round holes. There is a widespread myth that it was designed to fit in the currency trays used for that era's larger dollar bills, but recent investigations have refuted that. To compensate for the cyclical nature of the Census Bureau's demand for his machines, Hollerith founded the Tabulating Machine Company (1896) a predecessor to IBM. IBM manufactured a wide variety of business machines and eventually married the punched card to its early computers, encoding binary information as patterns of small rectangular holes. That IBM format eventually won out over the Univac format, which had used 90 columns of round holes.
The method is quite simple: On a piece of light-weight cardboard, successive positions either have a hole punched through them or are left intact. The rectangular bits of paper punched out are called chads. Thus, each punch location on the card represents a single binary digit (or "bit"). Each column on the card contained several punch positions (multiple bits), thereby allowing one column of the card to represent a digit or other character. Cards could be made in which every possible punch position had a hole: These were called "lace cards." The IBM card format, which became standard, held 80 columns of 12 punch locations each, representing 80 characters (since 12 bits is more than enough for representing a character, not all combinations were used.) originally coded: 1 punch (digit[0-9]) was a digit, 2 punches (zone[12,11,0] + digit[1-9]) was a letter, 3 punches (zone[12,11,0] + digit[1-7] + 8) was a special character, later the introduction of EBCDIC allowed columns with as many as 6 punches (zones[12,11,0,8,9] + digit[1-7]). Other coding schemes, sizes of card, and hole shapes were tried at various times.
The card readers used an electrical (metal "brush") or, later, optical sensor to detect which positions on the card contained a hole. They had high-speed mechanical feeders to feed hundreds of cards through in a very short time.
One of the key advantages of this system is that a computer was not required to encode information onto the cards -- the typewriter-like card-punch machine was all that was needed -- and "key-punch operators" (who did nothing but punch cards full-time on such machines) were in great demand. (Quality control was often having two different operators key the same data, with the 2nd using a card-verifier instead of a card-punch. If a card failed verification, the card-verifier would stop, letting the operator replace the card with a corrected one.) When the time came to transfer the information thus encoded into the computer, the process could occur at very high speed (either by the computer itself or by a separate device that "read" the cards and "wrote" the data onto magnetic tapes (or, later, on removable hard disks) that could then be mounted on the computer), thus making best use of expensive computer time.
Punched-card systems fell out of favor in the 1970s, as disk and tape storage became cost effective, and interactive terminals meant that users could edit their work with the computer directly rather than requiring the intermediate step of the punched cards. However, their influence lives on through many standard conventions and file formats. The terminals that replaced the punched cards displayed 80 columns of text, for compatibility with existing software. Many programs still operate on the convention of 80 text columns, although strict adherence to that is fading as newer systems employ graphical user interfaces with variable-width type fonts.
See also History of computing, computer storage, memory.
Some of the above material is based on FOLDOC.