However, the concept of a non-electronic calculating tool goes way back in history to early cave men. The first such tool is said to be a South African Lebombo which was a baboon's leg bone with notches carved into it and used as what is called a 'tally stick' or counting rod. Tally sticks were used when early man ran out of fingers on which to add up quantities. Throughout history thereafter similar devices have been invented from clay tablets to the traditional Roman abacus. Nearer the 20th century various scientists and mathematicians have developed a range of different counting machines.
The major transition to what we know as a computer today occurred when electricity came to be used as the power source for the machines. Previously, "computers" had relied upon mechanical or human power to turn handles and so on. With the introduction of electric power the stage was set for a major change. In technical terms we had moved on from analogue machines and into the digital age. The easiest way to understand the difference is to think of clocks. Analogue clocks have hands and a clockwork mechanism with gear wheels which turn the hands throughout the day. Power comes either from a wind-up spring or a weighted pendulum. A digital clock however displays numbers which are activated by electrical pulses. (NB. Strictly speaking you can now get digital/electronic mechanisms to turn analogue clock hands but I didn't want to complicate things!).
The other big innovation leading to computers we recognise today is the concept of programming. Programming is a way of storing up a sequence of instructions to the computer in such a way that, if you periodically re-run the programme, it will carry out the same actions without you having to input all the instructions again. In fact, even before electronic computers, there existed mechanical ones that ran from programmes. The most famous of these was the Jacquard Loom. In 1804 a French weaver names Joseph Marie Jacquard developed a loom in which the pattern of cloth being woven was controlled by a long paper tape consisting of card with holes punched in it. The trick was that the design could be changed by using a different tape without having to make any alterations to the loom itself. This was the forerunner of punched cards used in early computers and neatly demonstrates what a computer programme is. Here is a picture of a Jacquard loom.
You may be able to think of other devices that worked from interchangeable tapes or cylinders. Here is a selection showing a barrel organ, an automatic piano (pianola) and a record playing disc (musical boxes operating under the same principle as these disks but with cylinders). (Photographs courtesy of Wikipedia)
Into the modern age
One of the forefathers of the modern computer is regarded as Charles Babbage who is credited with inventing the first mechanical computer in the late 1880s. He called this his Difference Engine (see the Wikipedia photo below). Although some say that he invented digital programming he actually copied the idea of using punched cards from the Jacquard Loom (see above). The innovation was the use of separate parts of his engine - one to carry out the calculations and the other to store the answers. One of the notable collaborators in his work was Countess Ada Lovelace who was the daughter of the poet Lord Byron. It is believed that she enhanced his work with the concept of storable algorithms (programmes) and is said to be the creator of digital programming. Indeed, a later programming language - ADA - was named after her.