The word is derived from the Latin 'computare', which is composed of com- 'together' +putare 'to settle' (an account).
There is a myth that the word computer stands for 'Common Operating Machine Purposely Used for Technological and Educational Research'.
This is utter rubbish; for a start, the 'definition' does not make sense, and secondly, when computers where invented and named, they did exactly what their name suggests - they were gigantic calculators. They were rare and expensive devices that filled entire rooms.
That such a machine would have been named 'common' would have been ridiculous, let alone the idea that someone would use one for fun, or anything other than technological and educational research.
In 1943, Thomas Watson, the chairman of IBM, said that he thought there was "a world market for maybe five computers". This was, bear in mind, the man in charge of a computer company; and he was in change of making them sound good. It makes me wonder what else will change and become commonplace by the time he reaches his old age.