Turing equivalence, in the theory of computation, describes a computing device capable of performing the same computations as a Turing machine. Such a device is termed Turing equivalent. Here the same computations has a technical meaning, but in essence it means that both machines are equally useful, looking only at the results they produce.
A Turing machine is a reference for what is deterministically computable, and what is not. If a problem is computable with a (modern high-performance) computer, which is Turing equivalent, then it is also computable with a Turing machine. This is slightly misleading, though, since a Turing machine, while primitive, is assumed to have unlimited memory, which is true of no machine in the real world.
