Means it can do anything a Turing machine can do; mathematicians and computer scientists like that, because they've already proven a Turing machine can do most anything. But one characteristic of a Turing machine is infinite storage space, so a logical system (such as a high-level program language, or Life) can be Turing complete, but a physical machine can't ever. If you relax the requirement by accepting anything with some general-purpose store (and assuming that's infinitely large), any general-purpose computer is. A 4-function calculator isn't.