What is computer ?

A computer is a device that accepts  information  (in the form of  digital ized  data ) and manipulates it for some result based on a program or sequence of instructions on how the data is to be processed. Complex computers also include the means for storing data (including the program, which is also a form of data) for some necessary duration. A program may be invariable and built into the computer (and called logic circuitry as it is on microprocessors ) or different programs may be provided to the computer (loaded into its storage and then started by an administrator or user). Today's computers have both kinds of programming.

What is computer ?

Most histories of the modern computer begin with the  Analytical Engine  envisioned by Charles Babbage  following the mathematical ideas of  George Boole , the mathematician who first stated the principles of logic inherent in today's digital computer. Babbage's assistant and collaborator,  Ada Lovelace , is said to have introduced the ideas of program loops and subroutines and is sometimes considered the first programmer. Apart from mechanical calculators, the first really useable computers began with the vacuum tube, accelerated with the invention of the  transistor , which then became embedded in large numbers in integrated circuits, ultimately making possible the relatively low-cost personal computer.
Modern computers inherently follow the ideas of the stored program laid out by  John von Neumann  in 1945. Essentially, the program is read by the computer one instruction at a time, an operation is performed, and the computer then reads in the next instruction, and so on. Recently, computers and programs have been devised that allow multiple programs (and computers) to work on the same problem at the same time in parallel. With the advent of the Internet and higher  bandwidth  data transmission, programs and data that are part of the same overall project can be distributed over a network and embody the Sun Microsystems slogan: "The network is the computer."

Also see  analog computing .