a mathematical model of computation

As you possibly remember from school, a Turing Machine is a mathematical model of computation.

a theoretical machine that manipulates symbols on a tape strip, based on a table of rules

A Turing machine is a theoretical machine that manipulates symbols on a tape strip, based on a table of rules.

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 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 very simple computer

In essence, a Turing machine is a very simple computer.

a hypothetical machine thought of by the mathematician Alan Turing

A Turing machine is a hypothetical machine thought of by the mathematician Alan Turing.

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).

a theoretical machine that is used in thought experiments

In theoretical computer science, a Turing machine is a theoretical machine that is used in thought experiments to examine the abilities and limitations of computers.

an imaginary — not even quite hypothetical — computer

The Turing Machine is an imaginary — not even quite hypothetical — computer invented in 1936 by English mathematician Alan Turing (1912–1954) to help solve a question in mathematical logic.

an abstract machine capable of computation

A Turing machine is an abstract machine capable of computation.

a finite-state machine associated with a special kind of environment -- environment's tape -- in which environment can store (and later recover) sequences of symbols'

A Turing machine is a finite-state machine associated with a special kind of environment -- environment's tape -- in which environment can store (and later recover) sequences of symbols', also Stone 1972:8 where the word 'machine' is in quotation marks.

the template all computers today are based on

The Turing machine is the template all computers today are based on.

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 a tape of unlimited length that is divided into little squares.

a minimal idealization of a computer

A Turing machine is a minimal idealization of a computer.

a mathematical model of a mechanical machine

A Turing machine is a mathematical model of a mechanical machine.

a universal model of computation that defines a theoretical device that manipulates symbols on a strip of tape

A turing machine is a universal model of computation that defines a theoretical device that manipulates symbols on a strip of tape.

theoretical computer

A Turing machine is theoretical computer consisting of a finite set of internal states, a finite alphabet that includes a blank symbol, and a finite set of instructions.

a non-localized

In Victor’s Way terms: A Turing machine is a non-localized (i.e. abstract) set of rules that can simulate, i.e. copy, and so become, any localized, i.e. actual set of rules (read: boundaries or limits), whereby neither set rules is defined.

an infinite number of steps made up of a finite set of symbols

A Turing machine is one that follows a well defined process that could be an infinite number of steps made up of a finite set of symbols.