Falsifiability is a fundamental property of a statement of it being possible to have counter-examples to (the search for these counter-examples is called falsification). According to Karl Popper, claims that are not falsifiable are considered to be outside the realm of science. This criterion is accepted by most of the worldwide scientific community.
It is not a requirement of falsifiability that there be a current means of falsifying the theory. It must simply be logically possible that an observation or experiment could have done so, if it were not true. In cases where the theory is shown to be true, such as the Theory of Evolution, the means of falsification are exhaustively demonstrated to be incorrect.
Special creation is not falsifiable. There is no test which could show, even theoretically, that things were not specially created if they weren't. There is also no test which could show God didn't hire unicorns to create us if he didn't. Without falsifiability there are an infinite number of alternatives one can't prove, all of which have equal merit.
The Theory of Evolution is falsifiable. Had the fossil record been found to be static, it would have shown that species have not evolved. Had a mechanism been found that prevents, and has always prevented, genetic mutations from accumulating or being inherited, it would make evolution impossible. However, the opposite is true in both cases - those things were instead found to support the theory.