According to the Oxford English Dictionary, the first known use of "computer", as a word, was in the year 1613 in a book called The Yong Mans Gleanings by Richard Braithwait who was an English writer.
This usage of the term referred to a human computer, a person who carried out calculations or computations.
The word then continued with the same meaning until the mid 20th century. During the latter part of this period women were often hired as computers because they could be paid less than their male counterparts.
By year 1943, most human computers were women !
The Online Etymology Dictionary gives the first attested use of "computer" in the 1640s, meaning "one who calculates" .
The Online Etymology Dictionary states that the use of the term to mean "'calculating machine' (of any type) is from year 1897." The Online Etymology Dictionary indicates that the "modern use" of the term, to mean "programmable digital electronic computer" dates from "1945 under this name; [in a] theoretical [sense] from year 1937, as Turing machine".
A Turing machine is a mathematical model of computation that defines an abstract machine, which manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, and given any computer algorithm (set of instructions), a "Turing machine" capable of simulating that algorithm's logic can be constructed!