a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules

A Turing’s machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules.

a mathematical model not of computers, but of computation

The turing machine is a mathematical model not of computers, but of computation.

a theoretical computing system, described in 1936 by Alan Turing

A Turing machine is a theoretical computing system, described in 1936 by Alan Turing.

a general example of a CPU that controls all data manipulation done by a computer

A Turing machine is a general example of a CPU that controls all data manipulation done by a computer, with the canonical machine using sequential memory to store data.

a hypothetical computing device, first conceived by Alan Turing in 1936

A Turing machine is a hypothetical computing device, first conceived by Alan Turing in 1936.

a machine that can simulate any computer algorithm

(In short, a Turing machine is a machine that can simulate any computer algorithm (for those not familiar with Turing machines, check out this and this).

The simplest possible computing machine

The simplest possible computing machine is a Turing machine.

an abstract representation of a computer

The Turing machine is an abstract representation of a computer; a computer essentially manipulates bits; if you're familiar with micro-processor design you'll see that the analogy holds very well.

a theoretical device that consists of a tape of unlimited length that is divided into little squares

The Turing machine, developed by Alan Turing in the 1930s, is a theoretical device that consists of tape of unlimited length that is divided into little squares.

computers with a finite state machine that can interact with a tape of unlimited size

Turing machines are computers with a finite state machine that can interact with a tape of unlimited size.