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A function is said to be Turing computable if there exists a Turing machine that can compute it. In simpler terms, a function is Turing computable if there is an algorithmic procedure, represented by a Turing machine, that can take inputs and produce outputs according to the rules defined by the function. This means that the function can be computed by a mechanical process following a finite set of instructions.
Alan Turing introduced this concept in his work on computability, showing that any function that can be computed by an algorithmic process can be computed by a Turing machine, making it a fundamental concept in computer science and mathematics.
