"Generation" in computer talk is a step in technology.originally, the term "generation" was used to distinguish between varying hardware technologies but it has know become extended to include both hardware and software that together make up a computer system.
The First Generation: 1945-1956 (The Vacuum Tube Years)

The first generation computers were huge, slow, expensive, and often undependable. In 1946 two Americans, Presper Eckert, and John Mauchly built the ENIAC (Electronic Numerical Integrator and Computer) electronic computer which used vacuum tubes instead of the mechanical switches of the Mark I. The ENIAC used thousands of vacuum tubes, which took up a lot of space and gave off a great deal of heat just like light bulbs do. The ENIAC led to other vacuum tube type computers like the EDVAC (Electronic Discrete Variable Automatic Computer) and the UNIVAC I (UNIVersal Automatic Computer). The vacuum tube was an extremely important step in the advancement of computers. Vacuum tubes were invented the same time the light bulb was invented by Thomas Edison and worked very similar to light bulbs. It's purpose was to act like an amplifier and a switch. Without any moving parts, vacuum tubes could take very weak signals and make the signal stronger (amplify it). Vacuum tubes could also stop and start the flow of electricity instantly (switch). These two properties made the ENIAC computer possible. The ENIAC gave off so much heat that they had to be cooled by gigantic air conditioners. However, even with these huge coolers, vacuum tubes still overheated regularly. It was time for something new.
Mauchly and Eckert: The ENIAC
The first general-purpose electronic computer appeared in 1946. it was developed by John William Mauchly and John Presper Eckert. They called their machine the Electronic Numerical Integrator and Computer (ENIAC).
ENIAC--1946
Unlike previous counting tools, ENIAC had no mechanical parts, no counters, and no gears. it relied solely on vacuum tubes. Each vacuum tube contained an electronic circuit, a tiny pathway that carried electricity. Each circuit could turn on and off very much the way a light bulb does.
ENIAC operated 1000 times faster than Mark I. It could do 5000 additions per second and 300 multiplications. The cost of this machine was around 3 million dollars.
However, ENIAC had a number of problems. It's 19,000 vacuum tubes took up so much space that it required a room measuring 20 feet by 40 feet! The tubes also produced a lot of heat and were always burning out. On average, 50 tubes burned out each day. Today, for a few cents, you can buy one chip that has more computing power than ENIAC!
John von Neumann & the EDSAC--1949
In 1946 a mathematician named John von Neumann proposed two changes in computer design: (1) The machine's instructions, he said, should be stored inside the computer. (2) Because electronic circuits are either on or off, he suggested that people use a series of 0's or 1's to code all the information they put into the computer. A zero would stand for off; a one would stand for on. This code is called the binary code and is still used today.
The EDSAC (Electronic Delay Storage Automatic Computer) had 3,000 vacuum tubes and the programs were input using paper tapes.
Eckert and Mauchly & the UNIVAC--1951
In 1951, Eckert and Mauchly designed another computer called the UNIVAC (UNIVersal Automatic Computer). It was the first computer to be sold to businesses. UNIVAC contained 5,400 vacuum tubes and used magnetic tapes to give instructions to the computer. The UNIVAC was used to predict the presidential election of Dwight Eisenhower. No one believed the machines prediction at first, but it was very accurate.
The Second Generation: 1956-1963 (The Era of the Transistor)
The transistor computer did not last as long as the vacuum tube computer lasted, but it was no less important in the advancement of computer technology. In 1947 three scientists, John Bardeen, William Shockley, and Walter Brattain working at AT&T's Bell Labs invented what would replace the vacuum tube forever. This invention was the transistor which functions like a vacuum tube in that it can be used to relay and switch electronic signals.

There were obvious differences between the transistor and the vacuum tube. The transistor was faster, more reliable, smaller, and much cheaper to build than a vacuum tube. One transistor replaced the equivalent of 40 vacuum tubes. these transistors were made of solid material, some of which is silicon, an abundant element (second only to oxygen) found in beach sand and glass. Therefore, they were very cheap to produce. Transistors were found to conduct electricity faster and better than vacuum tubes. They were also much smaller and gave off virtually no heat compared to vacuum tubes. Their use marked a new beginning for the computer. Without this invention, space travel in the 1960's would not have been possible. However, a new invention would even further advance our ability to use computers.
The Third Generation: 1965-1970 (Integrated Circuits-Miniaturizing the Computer)
Transistors were a tremendous breakthrough in advancing the computer. However, no one could predict that thousands even now millions of transistors (circuits) could be compacted in such a small space. The integrated circuit, or as it is sometimes referred to as semiconductor chip, packs a huge number of transistors onto a single wafer of silicon. Robert Noyce of Fairchild Corporation and Jack Kilby of Texas Instruments independently discovered the amazing attributes of integrated circuits. Placing such large numbers of transistors on a single chip vastly increased the power of a single computer and lowered its cost considerably.

Since the invention of integrated circuits, the number of transistors that can be placed on a single chip has doubled every two years, shrinking both the size and cost of computers even further and further enhancing its power. Most electronic devices today use some form of integrated circuits placed on printed circuit boards--thin pieces of bakelite or fiberglass that have electrical connections etched onto them--sometimes called a mother board.
These third generation computers could carry out instructions in billionths of a second. The size of these machines dropped to the size of small file cabinets. Yet, the single biggest advancement in the computer era was yet to be discovered.
The Fourth Generation: 1971-Today (The Microprocessor)
This generation can be characterized by both the jump to monolithic integrated circuits (millions of transistors put onto one integrated circuit chip) and the invention of the microprocessor (a single chip that could do all the processing of a full-scale computer). By putting millions of transistors onto one single chip more calculation and faster speeds could be reached by computers. Because electricity travels about a foot in a billionth of a second, the smaller the distance the greater the speed of computers.
However, what really triggered the tremendous growth of computers and its significant impact on our lives is the invention of the microprocessor. Ted Hoff, employed by Intel (Robert Noyce's new company) invented a chip the size of a pencil eraser that could do all the computing and logic work of a computer. The microprocessor was made to be used in calculators, not computers. It led, however, to the invention of personal computers, or microcomputers.
It wasn't until the 1970's that people began buying computers for personal use. One of the earliest personal computers was the Altair 8800 computer kit. In 1975, you could purchase this kit and put it together to make your own personal computer. In 1977, the Apple II was sold to the public and in 1981 IBM entered the PC (personal computer) market.
Today we have all heard of Intel and its Pentium processors and now we know how it all got started. The computers of the next generation will have millions upon millions of transistors on one chip and will perform over a billion calculations in a single second. There is no end in sight for the computer movement.