Turing Completeness refers to a system's ability in computer science that can simulate a Turing machine, implying it possesses the computational power to solve any problem that a Turing machine can, given enough time and resources. This is the most basic kind of computing machine that is assumed in the theory of computation. A programming language or a cellular automaton, if Turing complete, can theoretically solve any computational problem, given sufficient resources. However, it doesn't provide any guarantees on efficiency or feasibility, such as runtime or memory usage.

The concept of Turing completeness originated from the works of Alan Turing in 1936. The term gained popularity and wider understanding during the and early 20th century, as the theoretical foundations of computer science were being laid.

The idea of Turing completeness is primarily attributed to Alan Turing, a pioneering British mathematician. His work formed the foundational concepts of theoretical computer science and computational theory, largely contributing to the understanding of Turing machines and the rules about their capabilities and limitations.